De Gea was granted leave to return to his native Spain for the birth of his first child, missing games against Manchester City and AC Milan as a result with Dean Henderson coming into replace him.
The Spain international returned to Manchester this week but has not trained with the rest of the squad, observing a period of self-isolation following his trip.
Those returning to the UK from Spain are required to self-isolate for five days.
‘David is back in Manchester,’ Solskjaer said.
‘So he is quarantining, or self-isolating. He is touch and go for Sunday I think, as I am not sure if it was Monday or Tuesday when he arrived back in Manchester.”
‘No, I think he has got to stay at home. I think so, he is not training with us anyway. It is different if you travel away and compete, so no he has not been training since he came back.’
Henderson impressed in goal against City last Sunday, starting the move that saw Luke Shaw double United’s lead at the Etihad.
‘Very disappointed to conceded with one of the last kicks of the ball, or head,’ Solskjaer said on Thursday evening.
‘That makes it harder of course, but it was always going to be going down to the second game there, anyway.
‘I’ve seen him [Henderson] save them, but it’s the structure that we lose. We dropped too deep and we get blocked off and they get the header on.
‘We should have attacked the ball with the men we had there.’