Mane looks set to sign for Bayern Munich this summer, with the German giants already making two failed bids for the Senegal striker, who has been a key figure in Liverpool's success story under Jurgen Klopp, making it clear he wants to go.
Yet Rush, who is Liverpool's all-time record goalscorer, has suggested the exit of one of the symbols of Klopp's side will worry fans still reeling from a harrowing end to the season that saw Manchester City pip them to the title and Real Madrid beat the Reds in the European Cup final.
With big doubts over the future of Mohamed Salah at Liverpool as he continues to stall on a new contract, Rush suggests the exit of proven performers is a big concern.
"What Liverpool need to be doing right now is strengthening their squad and letting Mane go isn't going to do that," Rush told the Sunday World at a
Gambling.com event in London.
"We need to prepare ourselves for how strong Manchester City are going to be next year, because they're already looking formidable.
"They're going to be stronger, so we have to be stronger, too. It's a big concern because nobody wants Mane to leave, especially with the form he's been in this year.
"I'm still hopeful that all three will stay - Mane, Mo Salah and Roberto Firmino - and I'm sure Jurgen Klopp feels the same, so let's hope something can be sorted out.
"If any of them were to leave, it would be a big disappointment, but we'd just have to look to the future regardless.
"The real strength of this Liverpool team over the last couple of years has been their strength in depth.
"I look at the bench in some of the games at the back end of this season and it was incredible. Signing Luis Diaz and Diogo Jota brought a new dimension to the forward line.
"You feel now that Liverpool are no longer relying on one or two players to win them a game, but that will change if Mane, and maybe even Salah, goes, so Liverpool need to be careful of losing players as that strength in depth will be impacted.
"Liverpool will need to spend a lot money to replaced players of that calibre, but it's not just about money. It's finding players who are as good as Mane and Salah and that won't be easy."
Manchester City have got their big signing in early this summer after winning the race to sign Erling Haaland and Rush suggests the Norwegian will take Pep Guardiola's Premier League champions to the next level.
"There's no getting around the fact that signing Erling Haaland is going to make Manchester City even stronger," he added.
"They tried and failed to sign Harry Kane last summer, so we always knew they were in the market for a new striker - and Haaland is the best out there.
"He doesn't have any Premier League experience, but he's still so young it's a signing for the future as well as the present.
"He's expected to start scoring goals right from the off, but even if he doesn't hit the ground running he'll get the time he needs to find his feet.
"City have so many good players around him it's difficult to see anything other than him scoring week-in-week-out, but I suspect the main reason they're signing him is to try and finally get over the line in the Champions League.
"For a young man, he's already got plenty of experience in the Champions League, and his record speaks for itself. Is he the missing piece of the puzzle when it comes to City conquering Europe? Quite possibly.
"When you look back at their semi-final first leg against Real Madrid, they missed a string of chances to put the tie to bed.
"Haaland would have gobbled up those chances and City might have won 6-3 instead of 4-3 and saw out that lead in Madrid. But things didn't work out for them and maybe that's why they've moved so quickly to wrap up the deal with next season's Champions League already in mind.
"It's pretty remarkable City are where they are without an out-and-out forward in their ranks, but Haaland will give them a more obvious focal point."
Ian Rush spoke to the Sunday World at a Gambling.com event.