The France international and his agent Mino Raiola are banking on an impressive tournament this summer to maximise his chances of a move to Juventus or Real Madrid.
Super agent Raiola has already confirmed he’s opened talks with Juve over a potential return to the Serie A giants.
Ideally, United also need to get Pogba back on the pitch after an injury-ravaged season, if they are to command anywhere near their asking price of £150m for their most valuable asset.
But as the £89m midfielder steps up his return from ankle surgery, Solskjær was asked to categorically confirm he would play for the club again.
The Norwegian said: “I'd like to say that, as soon as he gets fit, he'll be good enough to play for the team. And I'm sure Paul's desperate to play for us again.”
He added: “Paul's a footballer and he wants to play football. He knows he has to work hard now to get back to his best.
“He's been out now for so long now, it's a challenge for him as well to get back into shape.”
Pogba’s Old Trafford exit now looks inevitable after making just five Premier League starts this term.
The question is how much United can get for him - but Solskjær is already making plans for the future after signing Bruno Fernandes in January and planning moves James Maddison and Jack Grealish in the summer.
Meanwhile Scott McTominay and Fred have established themselves in Pogba’s absence.
“Paul's an important player for us, but we've also learned so much about the others,” said Solskjær. “Some other players have really stepped up and taken on this responsibility and shown what they can be and what they are for Man United.
“But it's unfortunate you get some of your best players injured, but that's just part of it, that's part of being here.
“You can't just say 'I feel sorry for myself because we've had all these injuries' – we're building a squad that can cope with this.”
Raiola has stepped up his campaign to get Pogba out of United in recent days.
He told Italian media: “He never lost his smile, but clearly a great player doesn't go to Manchester United only to not challenge for the Champions League or the Premier League title.
“It would be bull for me not to admit Paul wants to stay at the highest level.
“I talk to Juventus and their vice-chairman Pavel Nedved about many things, including about Pogba and other players, as is only right for a big club.
“You need to get information, see what's happening, put down a few hypotheses, dream a little.”
Solskjaer has consistently dismissed Raiola’s public comments – and ahead of Monday’s game with Chelsea, said: “I've not spoken to Mino, that's for sure. I haven't sat down and told Paul to tell his agent what to say, but Paul is our player and not Mino's.”