The Mirror says Shaw is in line to win a new long-term deal at Manchester United before the end of the season.
The England full-back appears to have won over manager Mourinho after a torrid couple of years under the Red Devils' demanding boss.
Shaw, 22, has struggled for game time since returning from a foot operation last spring, but is now back in the first team reckoning at Old Trafford.
Mourinho's public criticisms of the former Southampton starlet reached the point where teammates believed he was being treated unfairly.
But Shaw has since impressed in recent weeks and has a chance for a rare run in the side from now until the summer, with the Old Trafford giants planning to tie him down on improved terms.