Antonio Conte wants to help Harry Kane achieve all of his goals at Tottenham after the striker reminded everyone just how good he is with a devastating display in the 3-2 win over Manchester City – the club he was so desperate to join in the summer.

The England captain wanted to leave his boyhood club last year due to a lack of progress and the 28-year-old is understood to be waiting until the end of the season before committing his future to the club.

Conte, who accepts Kane and all of his players have the right to make the “best decision” about their future in the summer, is likely to be Tottenham’s best chance of keeping Kane happy. The pair have hit it off and Conte, who joked that Kane would play against Burnley on Wednesday even if he had only one leg, has vowed to improve the player.

Kane is desperate to win silverware with Spurs while he also wants to become both Tottenham’s and the Premier League’s all-time top scorer – both realistic targets. Conte said: “Harry is a player with great ambition and it must be this way because a player like him, I repeat, we are talking about a world-class striker.

“He has to be ambitious. For sure, for a player and for a striker, it’s very important to improve, to beat records. Records are important but, at the same time, it’s also important at the end of your career to lift trophies because only if you win and lift trophies can you go into the story of the club.

“My task in this moment is to try and improve him. But in the same way, with the other players, to become more complete. For sure, to improve a player to stay in this level is not easy because the space [to improve] is not so much. But I still think he’s improving a lot and Harry is another player who gives me great availability.”

Spurs’ best chance of getting back to the top table of English football is giving Conte the tools to succeed. But the Italian says he also has to convince the players he is the man to take them on the journey.

He said: “There is only one way to convince this sort of player. It is to work, it is to convince [them] of your football knowledge and to improve them. Only in this way you have the respect of your players.

“I have only this way to show to my players – I am here because we are trying to start to build something important together.”

Kane suffered a knock to his back at Manchester City, where he put in a dazzling display, scoring two goals and having a hand in the other. Kane’s importance to the Spurs side is obvious, even without considering they have no back-up striker, and Conte tapped into his humour to make the point.

“He had a hit in his back but he has to play!” the Italian said. “If he has one leg he has to play. Harry knows very well the importance he has on the squad for his personality, for his experience. But he is good.

“I am joking, I don’t force a player if he is injured to play. I only say that to tell you the importance of the player. He is good, he is ready.”