"Maybe the future might have been worrying him and that's part of the reason he's injured", said Solskjaer.
"I thought first half (in Wednesday's 1-0 Champions League defeat to Barcelona), yeah, we speak about Fred and Scott (McTominay), but I thought Paul made us play, settled us down a bit in the first half especially". "Just lately we haven't been ruthless enough when chances have arrived, and that has cost us points because I thing we should have won against Wolves and Arsenal".
Cole said: "Hopefully for Manchester United he stays because a fully fit, focused Pogba is only good for Man United".
The potential exits of all these players would free up a massive chunk of the club's wage bill and Ed Woodward is also reportedly keen to back Solskjaer with big money in the transfer window, as the club looks to bring in reinforcements in defence, midfield and attack.
Solskjaer, speaking to the press on Friday, insisted the player is happy too after praising his performance against Barca in midweek.
Harry Kane ankle injury update
Spurs said on Thursday that tests on Kane's injured ankle have shown " a significant lateral ligament injury to his left ankle ". He is Harry Kane because he behaves like this in the past.
Sanchez has not played since sustaining medial knee ligament damage during the 3-2 Premier League win over Southampton on March 2, but has now resumed full training.
"We have a certain standard here", Solskjaer said. I think now you are going to have to see the real Man United players come up. Maybe he is more likely for the Barcelona game.
Third place would guarantee United qualification for the Champions League - which by Solskjaer's calculation would mean beating at least one out of second-placed Manchester City and Chelsea, who they host in consecutive games at Old Trafford this month. "We want top three".
The manager has made clear that he and his coaching staff always knew they had a major job on their hands to revive the club on a long-term basis.
United are now in sixth place in the league, three points behind fourth-placed Tottenham and five off Chelsea in third, although they do have a game in hand. "Top four is also an aim if we don't get 15 - but we should aim for 15 points".