Spurs signed the Sweden international in January on an initial 18-month deal worth €10 million with an option for a permanent transfer set at €30m.
Kulusevski has made a huge impact at Spurs having registered three goals and six assists in 11 Premier League appearances, forming a key part of Conte's three-man attack alongside Harry Kane and Son Heung-Min.
Conte has long been an admirer of the 21-year-old with sources telling ESPN he was keen on signing the winger during his Inter Milan tenure and the forward is said to have settled in quickly at the north London club.
Spurs are already committed to making centre-back Cristian Romero's loan move from Atalanta permanent at the end of the season for a fixed €55m fee and signing Kulusevski in addition would represent a significant outlay before pursuing fresh targets.
But ESPN sources claim Spurs have a mandatory obligation to sign Kulusevski on a permanent deal in 2023 for a higher price if he plays in 50% of Tottenham's Premier League games next season, which is almost certain assuming he stays clear of injury given his importance to the team, and Conte is keen to resolve any uncertainty over the player's situation.
Spurs have won seven of their last nine League games to move three points clear of Arsenal in the race to seal fourth place and the final Champions League qualification spot.
Speaking about Kulusevski last month, Conte said: "We are talking about an important prospect. Probably he could explode in the future. Also because I can see the intensity, the will and the desire to play.
"As everyday in training sessions, he is a type of player who has it in his mind the target to become a top player in his career and as his manager I try to help him to improve and believe. For sure is he an important prospect for the present and for the future."