De Gea has missed Manchester United's last three games after returning to Spain to attend the birth of his first child.
As he left United's elite performance bubble, the 30-year-old is now self-isolating after returning to Manchester in line with UK government guidelines.
He will be allowed to rejoin training if he returns a negative COVID-19 test after spending an initial five days in quarantine meaning he could feature against West Ham at Old Trafford on Sunday.
"He is back in Manchester," Solskjaer said, who has handed Dean Henderson the gloves for United's last three games.
"He is self isolating. He is just touch and go for Sunday I think. I can't really know when he came back so I am not really sure if [he arrived back] on Monday or Tuesday.
"I think the rules are he has to stay at home. He is not training with us anyway. It's different if you travel away and compete so no he has not been training since he came back."
"I don't think any of those will be available," he said. "We hope before the international break but I am not sure. It has taken a little longer than we expected, so three games now and then the international break, then they will be available with us."
David Moyes' side have benefitted from the arrival of Jesse Lingard, who has scored four goals in six games since leaving United on loan, although the 28-year-old will not be eligible to face his parent club.
"For Jesse it's really worked out, for David it's really worked out and for us as a club as well because we know that Jesse's position is a 10 and we have got Bruno [Fernandes] there," Solskjaer added.
"For me it was a no brainer to get Jesse a chance to prove himself and play some football again. He has been really bright for them and he is finally back to himself."