Shaw is about to embark on a make or break year at United.
"Because he is a fantastic guy in my two years and with Mr. (Louis) Van Gaal before me", Mourinho said, as quoted by FourFourTwo.
The Armenia global said: "United was hard but you have to be ready for everything so I kept going".
But speaking on United's tour of the US, he revealed he has made a decision to stay unless Jose Mourinho tells him he is not wanted.
There have also been question marks over the 23-year-old's conditioning, as he enters the final 12 months of his contract at Old Trafford.
Shaw has endured injury, notably a broken leg in September 2015 that ended his season.
It was initially thought that Martial, who has expressed a desire to leave United this summer, received authorisation to dip out of the club's USA tour base in Los Angeles to be with his family.
Darmian has attracted interest from a slew of Italian clubs with Juventus believed to be in pole position, but Inter are also striving to take the defender back to his homeland.
Rare Celestial treat: Longest total Lunar Eclipse of century falls tomorrow
If you were standing on the moon at the time of the eclipse , the Earth would look like a black disk outlined in glowing red. Devotees of the Blood Moon Prophecy predicted that the world would end on September 28, 2015 (obviously, it didn't happen).
When and where to watch the Blood Moon in Sweden
But alas, for those of us here in North America, this lunation won't be visible since it will occur in the late afternoon. The eclipse will be visible to people in Europe, Africa and the Middle East on July 27 between sunset and midnight.
Manchester United Manager Jose Mourinho Aims A Big Dig At Liverpool
Dimitar Berbatov has tipped Manchester United to win the Premier League title under Jose Mourinho next season. Mourinho and Klopp will come face to face this weekend when Man United face Liverpool in MI on Saturday night.
Asked if he doubted his future after he was substituted at half-time of United's FA Cup clash against Brighton and Hove Albion last season, Shaw replied: "Not doubts, but there has been emotion".
"But I've worked hard on my fitness over the summer, not just because of the criticism and the pictures, I wanted to get in the best shape and that wasn't my best shape". The manager was probably thinking: 'Jesus Christ!'I said to my girlfriend: 'I've just opened it and I must look so weird now.' It was fine.
Despite Mourinho's public criticism of Shaw, the England worldwide said the Portuguese coach texted him in the off-season to spur him on.
"I will be [staying] unless something changes dramatically and the manager comes to me and says I'm not in his plans". Now I know what I need to do.
"It was a breath of fresh air when he texted me", he added. Shaw, though, says he's just got a big body. He says these things because he knows I can do it.
Which players are Manchester United most likely to sell and sign this summer, according to 888sport?
That doesn't mean to say that he hasn't still got a lot to offer at the very highest level, though. I'm used to it. "It still gives me confidence".