The London Evening Standard reports that Kane will be the subject of a £45m offer from Manchester United this summer after a stunning campaign for Spurs.
But Tottenham have 'no interest' in selling the forward, who has scored 31 goals so far this season.
Kane emerged as the Premier League's breakout star this campaign, starting the season on the bench for Tottenham's Premier League games before his hot form in front of goal in the Europa League prompted Mauricio Pochettino to promote him into the starting eleven.
And he hasn't looked back since, scooping the PFA Young Player of the Year award after becoming the first Tottenham forward since Gary Linekar to break the 30-goal mark in a single season.
Manchester United will have space in their squad for a new striker this summer, assuming as expected Radamel Falcao does not make his loan move permanent.
It may even be the case that Robin van Persie departs too. The Dutchman has been hampered with injury this season, and United boss van Gaal may opt to cash-in while he retains some sell-on value.
Van Gaal has been told by United chief Ed Woodward that he has licence to spend having splashed out £150m 12 months ago. And Kane would certainly be an expensive acquisition at £45m, albeit one who fits the squad profile - young, talented and with something to prove at the highest level.
That's what United have opted for in the £25m capture of Memphis Depay. The gifted winger is just 21 years old, the same age as Kane, and is yet to appear at Champions League level.
For Tottenham's part, they're desperate to keep the home-grown star at the club - but from Daniel Levy's point of view, a £45m offer may be too good to turn down.
It's certainly well above market value for a player with less than a season's track record of goalscoring success.
But what do you think Manchester United fans - would Harry Kane be a good signing? Even if you paid £45m?
Have your say below!