Pogba has entered the final year of his deal at Old Trafford and has been the subject of interest from Paris Saint-Germain.
If the club cannot agree fresh terms with the France international, he will be able to walk away for free next summer after also leaving United at the end of his contract when he moved to Juventus in 2012.
“Talks are ongoing between Paul’s representatives and the club representatives,” Solskjaer said, following a 4-2 preseason defeat to QPR on Saturday.
“All the dialogue I’ve had with Paul is that he’s looking forward to the season. There’s always speculation about Paul, the talks between the club and Paul’s representatives, I don’t know every detail of every single one of them. I’ve not got anything to say really about that.
“There’s always clubs being interested and of course we’ve seen Paul at his best and Paul knows what we feel about it and I’ve enjoyed my time working with him and hopefully we can work together.”
United announced on Saturday morning that Solskjaer has signed a new three-year contract to stay on as manager until at least 2024.
The Norwegian has already sanctioned the £72.9 million signing of Jadon Sancho from Borussia Dortmund and suggested there could be more new arrivals to follow before the deadline amid interest in Real Madrid defender Raphael Varane.
“You never say a team is complete,” Solskjaer said. “It’s always dynamic, always moving parts and you’ve got to be ready for changes.
“We knew this was going to be a rebuild and closer to a team I envisaged, attacking flair, pace and defensive solidity. Last season we went unbeaten away from home in the league, we scored goals and tightened at the back as well.
“It’s an honour to have the role of the manager and it’s continuing the work we’ve done with the staff, keep adding little things to improve and we’ve become a better team. Hopefully now we can take the next step and challenge for trophies.”
Elanga, 18, has impressed already this summer after scoring his first senior goal on the final day of last season and Solskjaer said he could have a role to play for the first-team when the new campaign begins in August.
“It would be easy to say the boy should go on loan but he’s doing so well,” Solskjaer added. “He’s electric, he’s got pace, skill and he’s got the courage and bravery of a Man United player.
“Today he created chances for others and himself. I wouldn’t be surprised if he’s going to be staying here. It depends, of course. It’s important for him to develop and get game time but he’s one that we’ve not really decided.”
Solskjaer added that defender Alex Telles will be out for a “few weeks” after sustaining an ankle injury.
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