The Red Devils boss has been heavily linked with a move for a left-back this month – Danny Rose, Ryan Sessegnon and Kieran Tierney have emerged as targets – but Shaw has made a significant impression on Mourinho recently.
Having fallen out of favour with the United boss last year, Shaw looked destined to leave Old Trafford in January, with a number of Premier League clubs said to be interested in landing his signature.
But the England defender has started five consecutive games for United and is expected to face Burnley this weekend despite the return of Ashley Young from suspension.
‘You like the transfer market, I can say that in this moment I don’t see many left-backs better than this Luke Shaw,’ Mourinho said on Friday, appearing to question the need for investment in the position.
‘He has 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 he was coming step by step, and now with a good run of matches and continuity, he is 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.’
Ahead of the weekend’s action, Zlatan Ibrahimovic and Eric Bailly remain sidelined for United, while Daley Blind will also miss the fixture with a ‘small problem’.
‘Just Eric and Zlatan, they are still recovering,’ Mourinho said when asked for team news. ‘Today we had not a big problem, a small problem with Daley Blind.
‘Nothing big but it stopped him to be available for this match. Apart from that everybody is fine and fit and strong and with desire to play.’