Speculation over the future of Kane, widely regarded as one of the best strikers in the world, was expected ahead of the summer transfer window.
Spurs have again failed to win a trophy, a drought now stretching into a a 14th year, and will again miss out on Champions League football next season.
Sky Sports reported on Tuesday that Kane has told the club of his desire to leave this summer and wants to remain in the Premier League.
When approached by Standard Sport for comment, Tottenham said in a statement: "Our focus is on finishing the season as strongly as possible. That’s what everyone should be focused on."
Kane has made no secret of his desire to win trophies and ideally would have prefered to win them with his boyhood club Spurs.
Back in 2017, Kane told Sky Sport that he would be "disappointed" if "in three years time" Spurs had not won a trophy.
A second-placed finish in the Premier League, and Champions League and, most recently, League Cup runners-up medals followed, but no silverware.
Manchester United, Man City and Chelsea are all reportedly interested in a deal to buy Kane, who could cost upwards of £150million with three years still to run on his contract.