Kane is in the final two years of his contract, signed in 2018, and failed to engineer a move to Manchester City last summer. The arrival of Conte as manager late last year, and the subsequent return to the Champions League, has softened Kane's desire to leave.
Standard Sport in May exclusively revealed that Kane - who on Sunday scored his 201st Premier League goal - is open to talks over an extension. The striker would be available for a cut-price fee next summer, when he also turns 30.
Asked if Kane has been offered a new contract, Conte replied: "I have to be honest with you: I don’t know, I don’t know about this situation, I don’t know the details, honestly, honestly. You know we are talking about an important player for Tottenham.
“The desire of everybody into the club is [for Kane] to continue with Tottenham, to sign a new contract. But if you ask me about the details, about information, I cannot answer you.”