Standard Sport understands that Spurs have no interest in selling their star man, and value him in excess of £200million.
However, Kane admitted in an Instagram Live Q&A last week he will consider his future if he feels that Spurs cannot match his ambition, saying: "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."
Man United are on the lookout for a striker this summer, and while both Ole Gunnar Solskjaer and Ed Woodward would jump at the chance to sign England's captain, Jadon Sancho remains their No.1 transfer target this summer.
With Sancho expected to cost over £100m - and likely closer to £120m - it seems unlikely that even United's transfer budget would stretch to a move for Kane as well.
One man who has made the switch from Spurs to Old Trafford is Berbatov, who went on to win to Premier League titles at United.
Joining this United side is not the same proposition as it was when Berbatov joined Sir Alex Ferguson's title-winning machine in 2008 - and while the Bulgarian knows Daniel Levy will demand a huge fee, he believes Kane will at least be considering a potential move.
Bernatov told Betfair: "This week I also saw some comments from Harry Kane, he loves Spurs but if they aren't going to be producing trophies then maybe it is time to leave. He knows all that, of course he's thinking about it, now even more than before.
"I think once it returns, maybe football will change in the amount of money that is spent, in the way players are bought and sold.
"If you are Kane in this situation and Daniel Levy is your chairman, he isn't going to sell you cheap, he is going to ask for what is fair, which in the case of Kane is a lot of money.
"I see a lot of similarities in the situation I went through and what is happening with Kane at the minute.
"There is a strong connection between Spurs and Manchester United, Teddy Sherringham was at Tottenham then went to Old Trafford, I was a Spurs striker and went to United and now Kane, who's also a striker, is being linked with a move there.
"I feel that it's also a similar time in his career that I was at, you start to think if you're on the right path and you think about winning things.
"If you are one of the lucky ones like Ryan Giggs, Paul Scholes or Gary Neville where you spend your whole life at one great club then you don't have to ask yourselves those questions, you just want to work hard and prove yourself everyday.
"When I left Spurs, even though I had won a trophy with the club it was a still difficult decision to make.
"I was following my own path and I knew that people wouldn't be happy, but I had to do it, I come from a small country and when one of the biggest clubs in the world came in for me it was my dream."