Reports surfaced over the weekend that Spurs would be willing to allow their prized asset to Manchester United for £200m, but it’s understood there is no truth in the speculation.
The future of Kane has come under renewed scrutiny during the last few weeks following an Instagram Live chat where the England captain refused to rule out leaving Spurs.
Kane said he would not stay at his boyhood club for the "sake of it" and wanted to see his side progress under Jose Mourinho.
"Obviously I get asked this question a lot," said Kane, in a chat on the social media platform with Jamie Redknapp.
"It's one of those things - I couldn't say yes and I couldn't say no.
"I love Spurs, I'll always love Spurs but I've always said if I don't feel we're progressing as a team or going in the right direction, I'm not someone to stay there for the sake of it.
"I'm an ambitious player, I want to improve, get better and become one of the top, top players.
"It all depends on what happens as a team and how we progress as a team.
"So it's not a definite I'm going to stay there forever, but it's not a no either."
Kane, who will be fit following a hamstring injury when the Premier League can resume after the coronavirus pandemic, has previously said he would be happy to stay at Spurs for the rest of his career.
But their slide in the last 18 months will have been disconcerting to the 26-year-old, with Mourinho's men crashing out of the Champions League and struggling to get back into it via the Premier League when the season ground to a halt.
Kane is approaching the peak years of his career and wants to add silverware to his collection of personal accolades, which include two Premier League and the 2018 World Cup Golden Boots.
However, Spurs have no intention of letting Kane go to Old Trafford or any other club when the transfer window reopens.
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