Kane, who captained his country in their last World Cup qualifier, has been a revelation since bursting into the Spurs first team under Mauricio Pochettino, and has proven himself as one of Europe's finest goalscorers over multiple seasons.
There are few pure number nines of Kane's quality and, crucially, age. United also love Robert Lewandowski of Bayern Munich but a serious investment in the Polish forward is difficult with him turning 29 this summer. 23 year-old Kane promises goals and longevity.
That said, reports in Sunday's newspapers that Mourinho was urging executive vice-chairman Ed Woodward to make a £100m move for Kane stirred little but laughter at White Hart Lane.
Tottenham would not countenance the sale of their most-prized asset regardless, but to do so for £100m several years after selling Gareth Bale for £86m is a laughable notion, given the inflation in the transfer market. Interestingly, some of the troubles of Bale's time in the Spanish capital have put Real Madrid off Kane a little, though they too have watched him and appreciate his talents.
Daniel Levy has a reputation as an unforgiving negotiator, one of the toughest in football, and any deal for Kane would not only need to be a world-record fee but closer to £200m than £100m.
Within the walls of Old Trafford they know this and the hope is that, if Tottenham were to fall away from being a perennial Champions League club, Kane might be more open to a move.
Within United's commercial department there is a feeling that Kane does not necessarily have the star quality of other recent United targets, with Antoine Griezmann the subject of publicity interest from partners long before his aborted move even began to gather speed.
Yet the same could be said for Kane as Wayne Rooney, who ultimately proved to be an immensely successful ambassador of the United brand around the globe.
That said, for now it appears clear that Harry Kane will remain with Tottenham unless Manchester United are willing to blow eye-watering amounts of money. And, even then, Daniel Levy may not blink.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies