Under Antonio Conte, Spurs have won five and drawn three of their eight games.
Harry Kane was involved in the project at the club after it appeared that he would leave, according to Antonio Conte.
Manchester City was interested in signing Kane last year.
The captain believed he had a gentleman's agreement with Levy to move on.
"He wants to give his all in every game and I am very happy with his commitment and the relationship we have created within the team," said Conte.
When Harry decided to stay at Spurs, I found a player completely involved in the project.
If we want to win or if we want to think to build something to win, Harry must be a point of start.
A meeting with Spurs to discuss transfers is pending.
Kane is under contract until 2024, and Levy made a great choice to keep the player.
Spurs have not lost in eight games since the head coach, Antonio Conte, replaced the sacked Nuno Espirito Santo.
Kane had only scored one league goal before the former Inter Milan manager's arrival, but he has now scored three times in his past four league games.
"You are showing that you want to continue to build something important around one of the best players in your team, and that's what you're doing," he said.
I followed the situation, but now it's not appropriate to look at the past. We have to live in the present because it says that Harry is a player at Spurs and is one of the best players in the team.
He is a point of reference in the dressing room. I am very enthusiastic about his involvement in the project.
The club hopes to end a 14-year trophyless streak when they face the Blues in the Carabao Cup semi-finals on Wednesday.
The Carabao Cup match between the two teams is not going to happen.
The League Cup final was won by Manchester City.
"I think that when they brought me here they wanted to send a signal to our players, and maybe also to the outside world," he said.
We have to try to create a situation where we can be competitive to try to win, that's what I think is important.
I think there is an important gap with other teams. Many teams are ready to win the title now. We have to work and try to improve.
