Last month, Pogba said this summer could be "a good time to have a new challenge somewhere else," fuelling rumours he could move to Real Madrid or return to Juventus, per David Hytner and Sid Lowe in the Guardian.
According to United manager Solskjaer, though, no club has made an official bid yet, and the Norwegian said Pogba could still be challenged by staying at United, per Goal:
"I've not been upset by anything he's said because we've had many conversations, and I know exactly what Paul is thinking. I can give him a new challenge. I've got to be careful—I can't dive into all this, hypothetical questions and all that. But we've not had offers.
"I can say the same about whichever player. If we don't get an offer for a player we would have to pay them out for them not to be here, don't we, so we haven't had offers. I've said so many times about Paul that he's a top, top boy and a great player and he's never, ever been a problem."
Pogba, 26, rejoined United from Juventus in 2016 for a then world-record £89 million fee, four years after moving from Old Trafford to the Old Lady.
The 2018-19 campaign was statistically the best of his career in terms of his goals contribution, netting 13 times in the Premier League and providing nine assists:
His best period of the season came in the two months after Solskjaer was appointed in December on an interim basis as Jose Mourinho's successor.
However, matching the fortunes of United as a team, after a remarkable boost following Mourinho's departure, Pogba endured an awful end to the season.
United lost just one of 17 in all competitions immediately after Solskjaer's appointment, but they then won just two of their final 12 games of the season.
It meant the Red Devils finished the campaign with no silverware and sixth in the Premier League, so they will play in the UEFA Europa League next season instead of the UEFA Champions League.
That is likely one of the key reasons Pogba is considering a move away from Old Trafford.
If Solskjaer can persuade him to stay, though, United will have a much better chance of breaking back into the Premier League's top four next season.