The Mirror says with his contract at Old Trafford due to expire next year, attentions are starting to turn towards a possible new contract.
Solskjaer wants the midfielder to stay at the club, having worked so hard to get him back to his blistering best.
But it's said that, behind the scenes, there's a split in opinion.
Some United board members are wary of meeting Pogba's salary demands with the player's agent, Mino Raiola, wanting his client to pocket £400,000-a-week.
United are said to value their midfielder at £55million.