During the opening months of the campaign, Shaw found himself down the pecking order at Old Trafford and the 22-year-old was linked with a move away from the club during the January transfer window.
However, Shaw has now completed 90 minutes in six matches in the space of a month, and Mourinho has claimed that there are few better left-backs than the England international.
At a press conference, the 54-year-old said: "He's played very well. He was already improving and playing well when I start playing him after that long spell without minutes.
"I remember the first time, in the Champions League, he was coming step by step, and now with a good run of matches and continuity also, playing like he did against Everton, two days after a previous match, he's good, solid. Physically much better, mentally much stronger, tactically understanding the game much better and what we need in different phases and circumstances,
"I'm really happy and [looking at the transfer market], I can say that in this moment I don't see many left-backs better than this Luke Shaw."
Shaw has made a total of eight starts and two substitute appearances this season and is expected to feature when United face Burnley on Saturday afternoon.