Assistant manager Mike Phelan hopes Jonny Evans will be available for the trip to Everton on 20 August.
The Northern Ireland international is training again after undergoing an ankle operation and could increase the options open to Sir Alex Ferguson at the back.
Chris Smalling is definitely out of the Barclays Premier League opener after surgery of his own but Nemanja Vidic's successful return from his long lay-off has already provided a major boost.
"Jonny Evans will hopefully be available when we get back," said Phelan. "He's back doing light work on the training ground. We hope he'll be available for the start of the season. He won't have had the games under the belt but, if he's fit and progressing well, we'll push him forward.
"At the moment, Chris Smalling is going to be a bit longer in his recovery. He's had a setback, an injury, and he's progressing slowly."