Pogba's contract expires next summer and his agent Mino Raiola is keen to profit off another transfer, but Solskjaer hopes the 26-year-old will stay at Old Trafford.
"I can't comment on discussions between players and the clubs but of course we want to keep the best players around the club," Solskjaer replied when asked if Pogba would be getting a new contract.
"We want to build a squad for the future. Scott [McTominay] and Nemanja [Matic] are similar in position but they are at different stages in their careers. One is at the start, one really experienced, and then we also need players in that mid-range group.
"Hopefully we can do something. I know that since Paul came back he is looking better and better, he is enjoying his football and let's see where it takes us."