The Tottenham forward has been in fine form once again this season.
And his performances in a Spurs shirt over the last three campaigns have seen him linked with a move away from north London.
Real Madrid are the most likely suitors, with president Florentino Perez keen to bolster his attacking line to compete with Barcelona.
However, the Spanish outfit may have competition in the summer.
According to Marca, Mourinho is desperate to sign Kane at the end of the season to replace £75m signing Romelu Lukaku.
The publication claims the United boss regrets signing the Belgian in the summer.
Instead, Mourinho wanted Kane to be his first-choice striker and the club were willing to double the player's wages.
However, the England skipper is preparing to ask for more time to decide his future.
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Marca reports Kane wants to know whether Mauricio Pochettino will remain at Spurs beyond this year.
The 24-year-old also wants to play at the new Tottenham stadium when it opens next season.
Madrid have been long-time admirers of Kane.
And with the futures of Karim Benzema, Cristiano Ronaldo and Gareth Bale all uncertain, Los Blancos may look to make Daniel Levy a bumper offer this summer.