Solskjaer speaks to the press on Friday morning as he previews Manchester United's upcoming fixture against Sheffield United in the Premier League.
He confirms that McTominay, who's limped off in Brighton win, is out for United's next 2 fixtures.
“Scott (McTominay) will be out for a little while still. He has not been training with us, he is still recovering and hopefully we can see him, maybe, around the time of Tottenham or City. He heals quickly, Scotty, but he is not going to be ready for Sheffield United or Astana, definitely.
Meanwhile, he also confirms Rojo will be also out for 2 weeks. And he believes Pogba will be back in next few weeks.
'Pogba is improving. Obviously he has been out and when you are in a cast for that long you do your muscle, so gradually you have to step it up. He has not started on his football work yet so it will still be a little while before we see him.
'He had another test and scan just at the start of the international break and it's not healed yet. He's stepping up the recovery so he doesn't have to have the cast on.
'He's been out for six or seven weeks so he's gradually stepping it up, walking, on the treadmill and bike. We hope to see him in 2019.
'We don't play basketball. I don't see many basketball players tackling ankles, twisting and turning with studs. He's not ready to train.'
'If you take three out of any top club they'll struggle. It'll take it's toll, of course. Fred has stepped up. We have to conjure a way of replacing them. Long-term we're looking at different positions but we are looking at midfielders.'
While Pogba and McTominay remain out of contention, Solskjaer has seen his ranks bolstered by the return to fitness of others.
Luke Shaw and Nemanja Matic are back in training, having sat out long periods of the season, while Axel Tuanzebe is also pushing for a recall.
Solskjaer will not be rushing his walking wounded into his starting XI, but is pleased to have more options at his disposal.
He added: “Of course it is always helpful when players are coming back and we have numbers in training.
“We shouldn’t expect too much of them because they have been out for a long, long time.
“Axel, the last game he played was Newcastle. Nemanja was injured in the international break that week. Shawy, or Luke, has been out for three months now, more or less.
“At least they are training, training hard, so if we can give them some game time then that will be good.”