Speculation about the 26-year-old’s future is rife at the end of his third season since returning to Old Trafford from Juventus in for a then world-record fee.
The World Cup winner was attracting interest from Barcelona last summer and fell out with former manager Jose Mourinho, although the interim appointment of Solskjaer brought a striking upturn in fortunes.
Things have tailed off in recent matches as talk about Pogba’s contentment at United reared its head, with Real Madrid strongly linked with a player they pushed strongly to sign in 2016.
Zinedine Zidane’s return to the Bernabeu helm has fuelled talk, while the wheels appear to be in motion with the kind of campaign often associated with the Champions League holders when they target a player.
“There might be a campaign, there might be press,” Solskjaer said. “You never know what there is, but in my talks with Paul he’s always been positive here.
“I don’t see a difference in him when I chat to him.
“So, he’s focused on performing and he’s a proud player, who always gives his best.
“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.
“We just fell away towards the end. But the effort that he put in physically was tremendous.”
Put to Solskjaer that Pogba’s statistics have tailed off dramatically, the United boss said: “I think he has made a difference for us in a few games, so has Romelu (Lukaku), so has Marcus (Rashford).
“There have been different players in different periods that have made the difference.
“When you’re at Man United, it’s not just about one player. And it’s not just about Paul.
“He had his highest ever output physically on so he’s never ran as much in a Man United shirt as Wednesday night. That was brilliant, the way effort and attitude is there.”
Pogba’s future is one of numerous subplots as the season comes to a close and attention turns to rebuilding.
Ander Herrera is planning to leave on a free transfer and club captain Antonio Valencia will depart in the summer, while there remains questions about Juan Mata’s future and the number of players United will bring in to close the gap.
“I’m under no illusions that this is not going to be plain sailing,” Solskjaer said when asked if the recent run of four defeats in five underlined the scale of the task.
“It’s going to be hard. It’s going to be only survival of the fittest or survival of the best. That’s how ruthless we have to be in the end.
“We need players here who are going to be able to take us forward.
“That means the culture in the dressing room, the inner justice, what we do every single day here to make us challenging (for the title) again because Liverpool and (Manchester) City, they’re two teams that are too far head at the moment from what we like.
“We played against a Barcelona team, which is one of the teams that sets the standard in European football, and we’re under no other illusion than it’s going to be hard work and there’s going be some tough decisions made by me, Mick (Phelan) and the club.”
There remains work to be done when it comes to nailing down assistant manager Phelan.
Brought in on a temporary basis alongside Solskjaer, Sir Alex Ferguson’s former right-hand man has yet to sign a permanent deal.
Solskjaer believes his future is closer to being resolved and wants Phelan to stay in his current role rather than becoming technical director, having been linked with a post that looks similar to his role with bottom-placed A-League side Central Coast Mariners.
“I want to work with Mick Phelan and I want him to do the job he’s doing,” the Norwegian said. “You know, sometimes in this country, we’re more concerned about what the job title is rather than what I do and what people do.
“What Mick does is more than just being an assistant manager, even if he is an assistant manager. He’s just a fantastic guy to have around.”