This is according to the Mirror, who understand United will make a move for the England international given any encouragement from the north London outfit.
Manchester United boss Louis van Gaal is reportedly desperate to bring in a new top-level striker this summer, with Wayne Rooney, Javier Hernandez and James Wilson currently the only recognised centre-forwards at the Dutchman’s disposal.
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United beat Kane’s Tottenham 1-0 in their Premier League opener on Saturday, but were toothless throughout the 90 minutes.
The Red Devils mustered one solitary shot on target, while the only goal of the game was an own goal scored by Spurs right-back Kyle Walker.
Tottenham unlikely to sell Harry Kane
Although Kane failed to score, the 22-year-old was a handful for Manchester United, who were fortunate that Chris Smalling produced a superb individual performance on the afternoon to keep his England teammate relatively quiet.
Kane, though, was still arguably the best player for Tottenham at Old Trafford and will have caught the eye of Van Gaal, who was already a big admirer of the gifted striker.
Earlier this summer it was reported that United captain Rooney is also desperate for Van Gaal to sign Kane - and urged the former Barcelona and Bayern Munich coach to submit a £40 million bid.
But it would take more than that to convince Tottenham chairman Daniel Levy to sell the man who scored a magnificent 31 goals in all competitions for Spurs last season.
Indeed, as the Guardian state, it could be impossible for Manchester United to prise Kane away from White Hart Lane before the transfer window closes on September 1.
Harry Kane would be a stunning signing
Some expect Kane to suffer from so-called ‘second season syndrome’ this season - but the Tottenham star has already proved his immense quality and would be a superb signing for the Red Devils.
Manchester United fans: would Harry Kane be the dream striker signing this summer? Have your say by leaving a comment in the box below!