Kane has been linked with a move away from Tottenham amid reported interest from Premier League champions Manchester City, Manchester United, Chelsea, Real Madrid and Barcelona.
Levy spoke to Tottenham's official website after appointing former Juventus sporting director Fabio Paratici as managing director, warning the London outfit will do what is right for the club.
"I am never going to talk about any specific player in public," Levy said as Tottenham remain without a full-time head coach following Jose Mourinho's sacking in April.
"All I will say is his frustrations in not winning are shared by me and all the fans and players. We all want to win."