Kane has made clear his displeasure with Spurs in recent weeks as the north London club still have a season without lifting a trophy and have failed to qualify for the Champions League.
Reports suggest the England captain has asked to leave the club, with Manchester City and Manchester United among parties interested.
City are on the hunt for a new striker this summer as they look to replace outgoing legend Sergio Aguero, with President Khaldoon Al Mubarak saying they are “confident” in finding a player to replace the Argentine.
United aren’t so desperate for a new leader after Edinson Cavani agreed to stay at the club for another season, but they are longtime admirers of Kane and can be urged to act rather than risk losing to a Premier League rival.
The 27-year-old would be a transformative signing for either club, but with his contract not expiring until 2024, any deal would be extremely difficult to strike.
Levy is a deemed difficult negotiator, as both clubs know from their previous dealings with Spurs, and he has warned Kane that he will protect the club’s interests this summer.
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“I will never speak of a particular player in public,” Levy said on the club’s official website while discussing the arrival of new general manager Fabio Paratici.
“All I will say is his frustrations of not winning are shared by me and all the fans and players. We all want to win.
“One of the things Fabio will face when he enters is who will be selected, who will be asked to look for other clubs.
“There is a market there. What we want and what other clubs want is not always possible to achieve. We will do whatever is right for the club.