Striker Kane, who has just under two years left on his existing deal, has begun the new Premier League season with a bang, scoring four goals in as many games to help high-flying Spurs take 10 points from a possible 12.
The situation is in stark contrast to 12 months ago when the England captain was unsettled and made a slow start to the 2021-22 campaign after a mooted move to Manchester City failed to materialise.
Head coach Conte feels Tottenham are on an upward curve and working hard to satisfy Kane's expectations.
"You know very well that you create the perfect time (for a contract extension) with a project," said Conte.
"If also the player understands that there is a right process, that everybody is going in the same direction, I think every single player wants to see this.
"And I think that Harry for sure is happy because he is seeing this type of situation.
"There is a vision, there is a direction and there is a unity to try to improve the team and also to improve the team at the level of his expectations."
Conte insists he is not privy to specific details about a possible new deal for Kane or involved in any potential negotiations.
With Wednesday evening's derby at West Ham marking the start of two games a week until the World Cup, the Italian is more focused on keeping 29-year-old Kane content and committed in the short term.
"My opinion is only one of a million opinions," he said.
"We are talking about a world-class striker and a player who in this moment is the most representative player for Tottenham. For sure I would like him to sign a new contract.
"But in this moment, for me it is very important to see him happy, totally involved with this season, totally involved with this project and in what we are doing. For me, this is the most important.
"Then it's a decision that the player and the club have to take."