The England captain was heavily linked with a transfer to Manchester City this summer but his efforts to push through a move failed to come to fruition and look to have contributed towards a below-par first half of the season for the forward.
Kane struggled for goals under Nuno Espirito Santo, who was sacked in November and replaced by Conte, and even now the striker has only scored nine times for Spurs in all competitions this term.
Yet a second goal in the Premier League this campaign and improved display on Sunday against Liverpool showed green shoots for the 28-year-old, who will aim to build on that when Crystal Palace visit on Boxing Day.
Conte said: “Harry has showed me great availability and showed me (he is) totally involved in the Tottenham project.
“I see him every day and I see that he is happy.
“He leads in the training ground, he leads in the dressing room and he leads during the training sessions in a fantastic way. I am happy for what I am seeing every day.”
After scoring 23 goals and claiming 14 assists in the Premier League last season, Kane has a lot of catching up to do if he wants to try and get close to those numbers during the current campaign.
Spurs boss Conte has already admitted it would be difficult to start a game without his star striker given the quality of the 28-year-old, who suffered heartbreak in the Euro 2020 Final with England in the summer.
I see him every day and I see that he is happy
Antonio Conte on Harry Kane
Tottenham visit Southampton two days after they host Palace and also face Watford on New Year’s Day, which will mark two years since Kane suffered a serious hamstring injury at St Mary’s following the 2019 Christmas period.
“I know this and it is difficult to start the game without Harry because he is a point of reference in our team,” Conte admitted when quizzed on trying to manage the fitness of the forward.
“For sure these days I speak with him, I speak with the players because I want to understand very well which is the real physical condition.
“If there is someone that has a bit of fatigue, it will be very important to have a good chat with the players because we have to manage this period. This period is not easy but not only for us, for all the teams in the Premier League.”
The topic of the congested fixture schedule would most likely have been raised during Thursday’s virtual meeting between the 20 top-flight managers and the division’s governing body.
But Conte added: “If I have to be honest, it was a meeting that we tried to speak and some coaches tried to speak, to ask about solutions but I think everything was decided.
“I think yesterday it was a wall and for this reason I also prefer to not go into it.”
Asked if it was a waste of time, the 52-year-old added: “I think so.
“Because when you have a wall in front of you, you can speak and ask what you want but every decision was (already) taken.”
Spurs have no new injury concerns with Cristian Romero and Ryan Sessegnon both still out with hamstring and muscular problems respectively.