The 26-year-old midfielder has been tipped to sign a new contract with Leeds in the summer but there is also serious speculation over his future at Elland Road.
He is the top midfield target for Aston Villa and West Ham ahead of the next transfer window and even Manchester United are also reportedly working on a deal to take him to Old Trafford.
The Red Devils are believed to be keen to pull off an audacious move to snare him away from their rivals Leeds.
In London, Conte is a big fan of the player and would like to have the opportunity to take him to Tottenham in the summer.
But it has been claimed Levy is unlikely to want to get drawn into a bidding war for the midfielder in the transfer window.
The Tottenham chairman does not want to go head-to-head with Manchester United and pay what the Red Devils are prepared to fork out for Phillips.
Conte wants to sign two midfielders in the summer but Phillips is unlikely to be the one joining him at Spurs.
