Zinedine Zidane has made no secret of his appreciation for Pogba, who said it would be a "dream" to play for the Real Madrid head coach during the international break.
Pogba and his United team-mates struggled in an underwhelming 2-1 Premier League victory over Watford on Saturday – Solskjaer's first match since being appointed manager on a permanent basis.
And amid Madrid's interest, Solskjaer praised Pogba as he outlined his plans for the France World Cup winner in Manchester.
"We want Paul to be both on and off the ball a good player for us," Solskjaer said.
"We want him to be influential with the way we play. Sometimes that means up as an eight into the box, sometimes to control the game, drop down deeper.
"Against Watford he had to drop down to get a hold of the ball. Every single game is going to be different until the end of the season.
"We haven't really nailed down one way of playing. We've got three or four different ways of playing. That's the beauty of Paul – that he can do both."
Solskjaer also responded to former boss Louis van Gaal's claims that United have been guilty of "park-the-bus tactics" under the Norwegian.