Pogba's future has dominated headlines throughout the season – the World Cup-winning Frenchman reportedly unhappy in Manchester and linked to former club Juventus and Real Madrid.
But Pogba, who has endured an injury-ravaged campaign, has been in fine form since returning from an ankle problem last month, striking up an exciting partnership with Bruno Fernandes in midfield.
Pogba is contracted to Premier League giants United until 2021, with the option for a further year, and Solskjaer is looking to negotiate fresh terms with the 27-year-old after Nemanja Matic and Scott McTominay re-signed.
"I can't comment on discussions between player and the club but of course, we want to keep the best players around the club," Solskjaer said ahead of Thursday's trip to relegation-threatened Aston Villa.
"We want to build a squad for the future and Scott and Nemanja are a similar position but at different stages in their careers. One at the start, one really experienced one.
"We also need players in the mid-range group. Hopefully we can do something.
"I know that since Paul's come back he's looking better and better. He's enjoying his football and let's see where it takes us."
Pogba has supplied three assists in 11 Premier League appearances for United this season.
United are fifth in the Premier League and can close to within a point of Leicester City if they beat lowly Villa on the road.