The France international's future has once again been called into question amid reports he has reached a stalemate in discussions over a deal to stay at Old Trafford.
Pogba is due to become a free agent in a little under a year's time and is now rumoured to be a €50million ($79.5 million) target for Paris Saint-Germain.
However, Solskjaer remains confident the 28-year-old, who has spent five seasons with United in his second spell with the club, will remain in place beyond this window.
"Talks are ongoing between Paul's representative and the club representatives," Solskjaer said. "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 Paul and his representatives. I'm not in the detail of every single one. I've got nothing to say about that really.
"Paul knows what we feel about it and I've enjoyed my time working with him and hopefully we can continue working together."
Pogba has yet to link up with United for pre-season training, having being given an extended break after playing four times for France at UEFA Euro 2020.
The ex-Juventus midfielder scored one goal and assisted another for France at the tournament, while his eight chances created were second only to Antoine Griezmann (10) among Les Bleus players.
Speaking after United's 4-2 friendly defeat to Queens Park Rangers on Sunday (AEST), Solskjaer suggested Pogba could link up with his United team-mates in the next couple of days.
"Many will join in training on Monday so they've got a few weeks to catch up," he said.
"That's unfortunately the way it is; every year where there is a tournament, we have to catch up. Hopefully, they've done the work we've told them to do when they're away."
New signing Jadon Sancho and fellow England internationals Luke Shaw and Harry Maguire, who reached the UEFA Euro 2020 final, along with Copa America finalist Fred will "return in about 10 days' time".
Solskjaer had already confirmed ahead of United's defeat at Kiyan Prince Foundation Stadium that full-back Alex Telles will miss "a few weeks" with an ankle injury sustained in training.
United's next pre-season friendly is against Brentford at Old Trafford on Thursday (AEST), followed by games with Preston North End and Everton before their Premier League opener at home to Leeds United on 15 August (AEST).