Mourinho has complimented Shaw for his improved performances this season and the player must feel convinced that he has earned a new deal, as he stated last summer that he would only sign United contract if he felt he had done enough to justify staying.
"Since I came to United it's been a whirlwind four years that have passed so quickly", he said.
He said on the club's official app: "I'm very proud and happy".
"There have been ups and downs".
Paul Pogba can "look a little bit lackadaisical", admits Gary Pallister, but the Frenchman is considered to be a "genius" with match-winning quality for Manchester United. From signing today now it's all about looking forward and to how much I can help the team and become a success again.
Injuries, form and fitness issues as well as a tumultuous relationship with Mourinho have punctuated Shaw's time in the north-west.
The 23-year-old has faced public criticism from José Mourinho and has been limited to 50 Premier League appearances at United in almost four and a half years by a serious injury, form and fitness issues.
Shaw revealed last month he almost lost the leg, while it would be almost a year before he made another competitive appearance.
The youngest player in England's 2014 World Cup squad appeared to have turned the corner courtesy of an important part in rescuing a last-gasp draw with Everton in April 2017, only for Mourinho to sensationally claim Shaw only played well because he was telling him what to do.
They have also been taken aback by the number of former players in the media as TV and radio pundits weighing into the debate with remarks which lack any sort of constructive criticism. "I was telling him just now, he was doing things in the second half because he was reacting to my voice".
The 43-year-old added that he feels the rival clubs are mocking the Red Devils.
"The latter is what people at Old Trafford want to see: I mean that ball he played for Fred against Wolves was a moment of absolute genius".
The news brings to an end a year of speculation about Shaw's future at the club, following a rumoured falling-out with Mourinho. "We have an unbelievable group of players and the talent we have is scary, there are a lot of young lads that are hungry for trophies".