The 22-year-old missed the latter stages of the 2016-17 campaign with ligament damage, but he has travelled with the United squad for their pre-season tour of the United States.
Shaw is undergoing his own personal training regime on tour, and the England international has said that he is "feeling really good" as he nears a return to action.
"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 told Man United's official website.
"I have been running on the treadmill, doing my leg weights, making sure my foot is strong, a lot of CV work to keep me in good shape. I am feeling really good. Watching the game today, I miss it and I want to be back out there as soon as possible and stay out on the pitch.
"I don't want to be too hard, but I think sometimes I am unfortunate with the injuries and especially with my leg. But I don't want to look back at that. This injury I have is an unfortunate one, but that is in the past now. I need to keep fit and I feel that this season I will.
"I feel this is my season to prove myself and I am feeling in good shape. In myself I feel confident. I want to show everyone that I believe in myself and show the manager that he can believe in me."