Shaw has featured in all three of United's pre-season fixtures so far and will be hoping to hold on to his spot when the club play league rivals Liverpool in the International Champions Cup on Saturday. I don't know if he fancies to be back for that and put himself to be available for the team or stay on holiday.
The 29-year-old Tottenham central defender has been linked with a move here for much of the summer given that he has only a year left on his contract in North London.
Mourinho also discussed his lack of options at right-back, with Antonio Valencia injured and new signing Diogo Dalot also on the mend from a knee problem. He made just five Premier League starts last season, and is looking ever more likely to be leaving this summer.
The club are determined he moves overseas, despite interest from Premier League rivals Chelsea and Tottenham.
When asked why Darmian was skipper for the match, which United won 9-8 on penalties after a 1-1 draw, Mourinho said: "Because he is a fantastic guy in my two years and with Mr. [Louis] Van Gaal before me".
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I was doing work, but I didn't realise I needed to push it a bit more.
"If I go, it's because the offer that another team makes will be good".
If you're going to play for Manchester United you've got to be able to handle one-on-one.
Darmian was given the armband against boyhood club Milan on Wednesday - the first time he captained United.