It was, he reveals, not just a straight fight between Paris Saint-Germain and Real Madrid to sign the 23-year-old who is universally regarded as the most valuable footballer on the planet. He also spoke to Liverpool.
"We talked a little bit, but not too much. We talked a little bit," Mbappe cautiously confirms, before adding that Liverpool actually had a greater chance of signing him when it was time for him to leave Monaco and before he joined PSG in 2017. In fact, he has never hidden his admiration for Liverpool or the football they play under Jurgen Klopp – and it does seem to be the Premier League club he would consider should he ever leave Paris.
Quite what it would have meant for their forward line had he signed this summer is another matter.
"I talked to Liverpool because it's the favourite club of my mum, my mum loves Liverpool. I don't know why, you will have to ask her!" he says, laughing and nodding towards his mother Fayzi Lamari, who is also chuckling. "It's a good club and we met them five years ago. When I was in Monaco I met them. It's a big club."
As are PSG and, of course, Real, who were left stunned, embarrassed and apoplectic by Mbappe's decision to sign a new three-year contract with the French giants when they believed he was destined to be theirs, having made it clear he wanted out of Paris last year and then ran down the final season of his contract. He could even have signed a pre-contract with Real in January, but instead they missed out on getting him for a third time.
Astonishingly, the announcement from PSG that Mbappe was staying led to Javier Tebas, the combustible La Liga president, declaring it was "an insult to football" and promising to file complaints to UEFA and even the European Union. PSG have hit back, saying it is a sign that the Spanish league is being usurped by France.
"Of course, it was between Real Madrid and Paris Saint-Germain in the end," Mbappe says as he explains that he made his final decision only in the middle of last week and called Real president Florentino Perez – rather that WhatsApp-ing him as has been claimed – as he also denies suggestions that he performed some kind of "U-turn".
He was then sworn to secrecy by PSG and did not even tell his team-mates – although he says they could surely discern from his happy mood he was staying – with some nevertheless finding out in the dressing room only before their final league game against Metz on Saturday. Lionel Messi and Neymar told him it was his decision.
"Everybody knows I wanted to leave for Real Madrid last year and I think it was a good choice to leave last year. But now it's different because I was a free agent," Mbappe explains, and it does appear to have been a significant factor in his decision. He really did not want to leave France for nothing.
"I was a free agent and it was important to give back to my country. If I had left I would have left as a great player but there is a sentimental part. I don't think my chapter is closed. Things were not over for me at PSG," Mbappe says, before adding: "I'm French and I know I'm important in the country, and when you are important, you have to think not only about football but about your life.
"I will be in France after my career. I will leave here [PSG], I will be with my family, my friends. The only thing I can say is thank you to all the Real Madrid fans and the club because they gave me all the love. It's amazing because I was only there for one week when I was 14 [to train]. I said to them good luck for the Champions League [final]."
Real face Liverpool in Paris on Saturday and Mbappe makes no bones about it: winning the Champions League has become an "obsession".
"Always an obsession for me, always," the France international says. "It's not because we didn't win it that I have to say it's a target. No, no, no. It's an obsession. You don't have to be scared to lose. No, I am not scared to lose. Maybe I will not win the Champions League next year, but it's an obsession.
"I won the World Cup [in 2018] and I hope to win a second one this year, maybe, but of course I want to win the Champions League. Just because I lost the final (to Bayern Munich) and semi-final (to Manchester City), I won't say it's just a target. I am not arrogant. I will try every year to win it because it's what I want."
As Mbappe talks, his family sit and watch. Just as they did five years ago, in a different suite in the stadium, when he signed from Monaco and I was the first writer to interview him - even before the press conference unveiling. We called him the Prince of the Parc des Princes. Now he is the king. It is why, to complete the circle of renewing his contract, I have been invited back to talk to him.
Much has changed in the intervening years, although he is wearing a similarly sober suit, and not least with his 15-year-old brother, Ethan, who is also a player for PSG. Ethan, like the rest of the family, including his father Wilfried, is listening intently as Kylian talks in perfect English. He has taken language lessons as part of his determination to be a global superstar – and "superstar" is a word he is not afraid to use about himself.
"You can be a superstar and be yourself. It's what I am. I am myself," Mbappe says. "I am relaxed. I know I have to do some things because it's for the football or for the business or because I am famous. But when I go home I am a normal guy. I am Kylian, I go with my friends. I take care of my family. I am like you, a normal guy. When I go out I am not a normal guy though."
As Mbappe speaks, the noise can still be heard of hundreds of PSG fans congregated outside in the teeming rain singing his name. In a team full of superstars, with Messi and Neymar, he is indisputably the club's most important player.
In a difficult campaign which ended with yet more Champions League disappointment, knocked out by Real, inevitably, in the last 16 despite Mbappe scoring in both legs, he has carried the team with 36 goals in 45 games.
For the third season in a row, he was named the best player in Ligue 1 and at 23 has already won five French titles, three French Cups and two French League Cups as well as the World Cup. Mbappe has scored 168 times for PSG in 268 games and, with his dynamic style, pace and dribbling, it is not just about the goals.
Still his god-like standing with the fans represents an incredible transformation from provoking their fury as he tried to force his way out last summer only for PSG to turn down Real's offer of €180 million – pretty much the same amount paid for him – even though it meant they risked losing him for free. But PSG never gave up hope.
There is one topic which really animates Mbappe, though, and that is money.
He – and PSG – are annoyed at suggestions coming out of Spain that it was the finances, and his demand for control of image rights, that swung it. He is absolutely adamant that is not the case.
"It's quite funny for me. Until March there was not a single drop of ink written about image rights," he says, and insists he barely spoke to PSG president Nasser Al Khelaifi about money. Indeed, Al Khelaifi claims of Real: “I think they were prepared to pay a little bit more than we were.”
“I am a little bit sad because since I played football I showed everybody that I have the passion to play,” Mbappe says. “Every time people talk to me I talk about football, I talk about titles, I talk about big games. I never talk about money. People can talk about whatever they want. But everyone who knows me and when I talked to Real Madrid, I talked to Paris Saint-Germain and I never talked money. Not once. I never talked money with Nasser. My lawyer did, my mum did for a few minutes. But not me. I talked about sport because it's me on the pitch and I don't count money in my account. I don't care. I am here to win titles, to show I am the best and to be happy and I am happy right now.”
Such was the intense interest, the almost obsessional interest, in Mbappe's future that it became a topic of conversation for French president Emmanuel Macron. Even he attempted to persuade Mbappe to stay in France.
“It is something special. I never imagined to talk with this guy about my new contract," Mbappe says.
"It's amazing to talk to the president, to all these important people. At the end, it was my choice. They gave me good advice and I can only say thanks to them. My choice was to stay, to stay in my country, because I am French. To stay in the new project, in the new era, of Paris St-Germain and I think I made a good choice because it's my choice.”
PSG have Mbappe for at least the next three years – he insists that is the case, as do the club, and politely points out that release clauses are not allowed in France – with PSG now convinced he will never leave.
He also wants to put the record straight on wild claims that he will have some say over who PSG sign and also that he has demanded the captaincy.
“I am a football player first and foremost. I am part of a team and part of a squad,” he says. “We all have different status but I am a football player and won't go beyond that function. I am a football player, that is it.
“With regards to being captain, we already have a captain (Marquinhos), an important player, and I don't need to be captain to give my point of view and show exactly what I am made of on the pitch.”
Wherever he plays, though, Mbappe's ambitions are clear, having stated he wants to be the “best”. What does that mean to him?
“To be the best? It's to write history,” he says. “To win important titles collectively and individually. To give pleasure to people because football is not just about titles it's about emotion. It's about feeling. It's not just about scoring goals or winning the Ballon d'Or or the Champions League. It's about showing a lot of things, even off the pitch.
“To be respectful, to be yourself. It's global when I said to be the best. It's why I don't say to be the best player in the world.”
Some would say Mbappe already is that. He was certainly the most coveted, as Real have been left to ponder ruefully while PSG celebrate.