Real Madrid are reportedly keen on securing the services of the World Cup winner after Zinedine Zidane made him his prime target for the season to bolster his midfielder for the new LaLiga season.
And Pogba, following United’s 4-0 win over Chelsea in the season opener, disclosed there are still question marks surrounding his future at the club.
But Solskjaer, who previously promised the 26-year-old of a new challenge this season is adamant his star man will not depart the side.
“You [the media] always put question marks around Paul," Solskjaer said. "I don't think it's odd saying enjoy playing, I have fun with my team-mates, I enjoy what I'm doing, I love my job and enjoy the game.
"Of course that sentence with the question mark about him, there's always question marks about Paul.
"There's not one press conference that I've not answered a question about Paul Pogba – 80 per cent of what he said was that he enjoyed that game and his time here.
"I've got absolutely no concerns on Paul. For me, yeah, he's going to stay."
Manchester United will play Nuno Espirito Santo’s Wolves later today in their second game of the season at Molineux Stadium.
Enjoying his best season at United since arriving from Juventus in 2016, Pobga was the highest goalscorer for the club last season, scoring 13 goals with nine assists in thirty-five Premier League appearances.