Solskjaer's midfield options have been further depleted following the injury to Pogba, the France global having failed to feature since the draw with Arsenal in September as he recovers from an ankle problem.
Spanish radio station COPE claimed that the France global has been refusing to feature for the Red Devils in a bid to force a January move to Real Madrid.
Solskjaer is excited to have the midfielder back at his disposal and, while Sunday's visit of Aston Villa will come too soon for Pogba, the United manager would not rule out the prospect of having the player back to face former boss José Mourinho and his Tottenham side next Wednesday.
"Every player is allowed to be injured when he's injured and Paul is working hard to get back", he said, according to the Irish Examiner.
"He's a footballer and he's one of the best midfielders in the world and [having him back] will be like signing a new player before the transfer window opens".
"And, of course, we've missed him when he's been away".
Scott McTominay is pushing to play against Aston Villa as Manchester United return to Premier League action on the back of the 6,000-mile round trip to Kazakhstan.
"He's stepping up his recovery and let's see how soon he'll be match-fit and available".
"The truth is I feel at home here", De Gea said. I've been very pleased with Brandon, he scored a great goal, so let's see where they're at.
Manchester United provisional squad: De Gea, Romero, Grant, Wan-Bissaka, Young, Jones, Laird, Lindelof, Tuanzebe, Maguire, Shaw, Williams, Fred, Garner, Gomes, McTominay, Matic, James, Lingard, Mata, Pereira, Chong, Greenwood, Martial, Rashford.
"We hope Scotty will be back as soon as possible", Solskjaer added.
Pogba joined United for a club-record £89m in 2016 and has since made 148 appearances for the club.