Levy returned from the Bahamas, where he spent time with Spurs owner Joe Lewis on Sunday and met Conte and Paratici on Monday.
It is understood the trio agreed to make a right wing-back – with Paratici in talks over a move for Wolves’ Adama Traore – a midfielder and an attacker their top targets this month.
Conte would, ideally, also like to sign a new central defender, but that may have to wait until the summer, unless an opportunity arises.
Other than discussing transfers, Conte delivered his verdict on the current squad, which is unlikely to have made for comfortable listening for Levy, who has admitted the club’s recruitment must improve following four-and-a-half years of mismanagement that has resulted in a big gap opening between them and tonight’s opponents Chelsea.
After last week’s 2-0 League Cup semi-final first-leg defeat, Conte described the level of Tottenham’s squad as “middle” and revealed that the club are prepared to loan out, or sell, record signing Tanguy Ndombele, who was booed off the pitch during the FA Cup comeback win over Morecambe.
Ajax are interested in Steven Bergwijn, but the Dutch club have yet to get anywhere near Tottenham’s valuation, while Spurs are also open to selling or loaning out Matt Doherty and Dele Alli, while Harry Winks has done enough to convince Conte that he should stay.
“With Paratici, I have the possibility to speak every day, so to have the possibility to speak with our chairman, it was important,” Conte said.
“Also, because I like to have this type of relationship, to be honest and to always tell the truth.
“The club asked after one month to have a meeting and I said no, I preferred to have another month to make the right evaluation.
"It’s honest, to give more time to me and also the players, to show me who deserves to stay here. Now the situation is very clear.”
AC Milan midfielder Franck Kessie is out of contract in the summer and has attracted Spurs’ interest.
Tottenham’s decision to push forward with a move for a right wing-back, with Traore talks ongoing, underlines the mistakes that have left Conte struggling to bridge the gap with Chelsea.
Since selling Kyle Walker to Manchester City for £50m in 2017, Spurs have signed three right-backs and sacked three managers.
Mauricio Pochettino signed Serge Aurier for £23m, Jose Mourinho spent £14.7m on Doherty and Nuno Espirito Santo was in charge when Spurs paid up Aurier’s contract to make space for Emerson Royal, who, sources claim, Barcelona still cannot believe Spurs offered to pay £25.8m for.
Should Tottenham match Wolves’ £20m (€24m) valuation of Traore, they will have spent £83.5m (€100m) on right-backs, having recouped a combined £70m for Walker and Kieran Trippier, who joined Atletico Madrid for £20m in 2019, after which Spurs blew £53.8 million on Ndombele.
Conte chose not to comment on the 25-year-old. “I think it’s not right to speak about this type of situation,” he said.
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