The England international, out for the past four months with an ankle problem, lasted an hour of the second-string side's 1-1 draw with Swansea City Under-23s on Monday night.
After getting 60 minutes under his belt at Leigh Sports Village, along with fellow returnee Ashley Young, Shaw believes that he is ready to start challenging for a starting spot in Jose Mourinho's title-challenging squad.
"I'm feeling really good and I only push on from here," he told MUTV. "I'm looking for the first-team spot now, I'm going to keep pushing, and when the manager needs me I'm going to be ready. Whenever that is, I'm really looking forward to it.
"I'd rather it was sooner rather than later, but I'm feeling good and whenever I'm called upon, I'm ready. I was very happy to get an hour tonight – it was very important for me and for Ashley [Young] to get the minutes after the rehab we've had.
"It was a very positive 60 minutes – me and Ash both feel good. I feel very good and hopefully I can push on now, keep myself fit and get stronger and stronger."