Shaw has been one of United's more impressive performers during a disappointing start to the campaign which has seen the Red Devils lose two of their opening three games for the first time since 1992-93.
Mourinho has often been a vocal critic of Shaw in the past, but he was full of praise for the defender and urged him to keep up his recent level of consistency following his return to the international fold.
"It's a big week for him that hangs on a very important match with Burnley. He's played three very good matches and that's not easy to do when your team loses two of them. He had that balance and consistency, especially against Brighton in a bad team performance," Mourinho told reporters at a pre-match press conference.
"If next week his manager decides to give him minutes against Spain or Switzerland that would be very good for him. At the minute that's a result of the hard work, he and the coaches have done.
"A proper player is player of consistency. He's mentally and physically stronger and tactically he has a better understanding. We are very, very happy with him. To the national team after three Premier League matches, is extraordinary for him."
Shaw has not played for England since March 2017.