Shaw has attracted public criticism from Mourinho in the past, but the United manager has suggested there is no need to seek out a replacement for him after an upturn in form.
He [Shaw] played very well," said Mourinho. "He was already improving and playing well when I started playing him after that long spell without minutes.
"Now with a good run of matches and continuity, playing like he did against Everton - two days after another match - good, solid, physically much better, mentally much stronger, tactically understanding much better the game and what we need of him.
"I'm really happy and, you like the transfer market, I can say in this moment I don't see many left backs better than this Luke Shaw."