Rumours over the club's star striker have been rife amid another disappointing season for Spurs, whose last hope of silverware vanished with Sunday's EFL Cup final loss to Manchester City.
Kane is the leading goalscorer in the Premier League this season with 21 from 30 games, and his 125-minutes-per-goal ratio better than he has achieved in the previous two similarly prolific top-flight campaigns.
The England captain was named Premier League player of the year at the London Football Awards on Tuesday but pointedly said trophies were more important than individual honours.
"I want to be winning the biggest prizes that there is to offer as a team and we are not quite doing that," he told the Evening Standard.