The former Chelsea manager has been widely tipped to succeed the Dutchman during the Red Devils' poor 2015-16 campaign, and he reportedly believes there is a "gentleman's agreement" in place for him to take the top job at Old Trafford, per the Manchester Evening News' Samuel Luckhurst.
If and when Mourinho becomes United boss, he will undoubtedly make several changes among the playing personnel, and recent reports have indicated he is eager to sign Kane, per MEN's Luckhurst, James Dixon and Rob Pollard.
Kane, 22, would be a fantastic addition to the United attack after proving this season that he is capable of scoring on a consistent basis in the Premier League.
He has followed up his 21-goal breakout season in the 2014-15 English top flight by netting an impressive 21 times already this term, per WhoScored.com.
As noted by Bleacher Report's Dean Jones, he has emphatically proven the doubters wrong who thought his form last term was just a flash in the pan:
With the career of Wayne Rooney, 30, now on the wane, and Anthony Martial and Marcus Rashford still both very inexperienced in the Premier League, the addition of Kane would be a savvy move for United given he looks set to be a star for perhaps the next decade.
It is not the first time Kane has been linked with United—he was a target for them last summer as well, per Sky Sports.
It may be a challenging signing for United to pull off, though, even if Mourinho is at the helm at Old Trafford.
Will Harry Kane join Manchester United in the summer?
Kane has previously stated he sees his long-term future being at White Hart Lane, per MailOnline's Ian Ladyman.
And currently his prospects look better if he stays at Spurs than if he were to move to United. Mauricio Pochettino's side are still pushing Leicester City for the Premier League title and, unlike the Red Devils, look fairly certain to be playing in the Champions League next season.
United's derby defeat of Manchester City on Sunday has given them a better chance of finishing in the top four of the Premier League this season, but so inconsistent have they been under Van Gaal that it is far from a certainty.
United would be able to offer Kane a huge contract, and he may well be attracted by the prospect of working under Mourinho, but the Englishman is surely likely to remain at Spurs for some time yet.
Elsewhere, United's No. 2 goalkeeper Sergio Romero said he will remain at the club.
Signed by Van Gaal last summer when David De Gea looked set to depart for Real Madrid, Romero has spent most of the season on the bench as the Spaniard ended up staying put at Old Trafford.
Romero has been linked with a move to River Plate in his native Argentina, but the 29-year-old has now insisted he wants to remain at United and fight for a starting spot, per ESPN Argentina (via the Express' Charlie Phillippe):
No one talked to me, they took it from the press and nothing else, my head is placed in Manchester. In the matches I played, I’ve proved I can play. The dream of mine is to grab this place and defend it, and it doesn’t cross my mind to come to Argentina.
De Gea is one of the best goalkeepers in the world and is unlikely to concede his No. 1 spot to Romero while he remains at the club.
However, the Argentina No. 1 is more than capable and remains a very good backup for De Gea at United, thus his commitment to staying at the club can only be good for the Red Devils.