De Gea was substituted at half time with the scoreline at 2-0 and was replaced by Dean Henderson at St Mary’s after colliding with the post while trying to save James Ward-Prowse’s free-kick.
The 30-year-old was expected to be a doubt for Paris’ visit to Old Trafford but trained with the rest of the first-team squad at Carrington on Tuesday and could be in line to start in United’s penultimate Group H outing.
“David trained well so he’s available for selection,” said Ole Gunnar Solskjaer, who suggested that his squad almost has a clean bill of health for Wednesday night.
Anthony Martial has recovered from an illness which prevented him from taking part against Southampton, while Alex Telles and Paul Pogba are also in contention to play after recovering from a knock and an ankle injury respectively.
“You know it's going to be a challenge every time you have the Champions League nights to keep players away,” Solskjaer said. “Because they all want to be fit [to play] and everyone has been on the training pitch today.
“We're looking good. I think all of them are champing at the bit. David trained well today, as did the rest of the group. It was a good session.
“Anthony got through the session and felt okay, so he's also available for selection.”
The visit of Paris is likely to come too soon for Luke Shaw, who is still recovering from a hamstring injury, while Phil Jones is a long-term absentee.
“Luke is probably the biggest doubt but the rest of them are holding their hands up saying: 'I'm ready',” Solskjaer added.
“Luke isn't too far away so let's see what we do with him for tomorrow. Then, of course, Phil [Jones] has been away for a long time but now we're getting more and more players ready to participate in every game.”