The left-back remains on the treatment table as a result of his ankle ligament damage sustained late last season.
However, Mourinho opted to take the 22-year-old on United’s US tour as he continues his recovery.
The boss claimed last week: “We have players that belong to the squad but cannot play for next few months, [Marcos] Rojo, Ashley Young, Luke Shaw, if Zlatan [Ibrahimovic] stays.”
Express Sport understands Shaw will be given one last chance to save his Old Trafford career this term.
The defender was publicly criticised on separate occasions by Mourinho, leaving his future in doubt.
But while he focuses on getting back fit again, Shaw insists he has the full support of the Portuguese.
“When me and Ash tend to finish our sessions, we go over to see what the other players are doing and we see him (Mourinho).
“He asks how I am, how it is going and he keeps on top of how we are and to see how far along we are. He’s been great.”
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Manchester United stars were snapped attending an exclusive Adidas event after their pre-season win over LA Galaxy
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Rashford, Tuanzebe, Mkhitaryan and Darmian with model Emily Ratajkowski
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I haven’t got a timescale but I am feeling really good, working hard and the sooner the better
Shaw has been sidelined for nearly three months now, having last featured in Manchester United’s 1-1 draw with Swansea on April 30.
On when he could return from injury, Shaw added: “I have been doing rehab each day and it is coming along really well.
“I haven’t got a timescale but I am feeling really good, working hard and the sooner the better. Hopefully it is soon.”
Shaw will be looking to be back in action in time for when United kick off the new Premier League season at home to West Ham on August 13.