The French midfielder is set to leave United in the summer, yet the English club is determined to not let him go easily, and want to get a significant part of the transfer fee that they paid for him to Juventus in 2016.
Pogba has been performing much more consistently over the past few games, with the Frenchman playing brilliantly and helping United go level on points with Liverpool, particularly with a great performance against Aston Villa on New Year's Day.
Pogba's contract will end in 2022, and this summer is the biggest chance for United to get something for the 27-year-old, as he will be able to leave on a free in January 2022.
Calciomercato claim that Solskjaer has no desire to sign either Ramsey or Costa from Juventus.
Ramsey has not lived up to the heights expected of him ever since he moved to Juventus from Arsenal in 2019, and Costa has been linked with moves away for a long time, leading to his loan back to Bayern Munich this summer.
Arsenal have been linked with signing Ramsey, who value the Welsh midfielder much more highly than Solskjaer does.
There are questions whether Juventus can actually beat Real Madrid to signing Pogba, with the Los Blancos being extremely keen on signing the Frenchman, especially with Zinedine Zidane being a very big admirer of him.
Manchester United star Bruno Fernandes jumped to the Frenchman's defence on Friday after the 2-1 win against Aston Villa, saying "I think Paul was top on Friday night. We know all the qualities he has. That is not in doubt."
"We know he can play, we know he can help us and he was involved in both goals. For the first, he shows very good skill."
"He will give more and more and more with the confidence coming game after game."
Solskjaer also claimed the Pogba is getting better, saying that he is "getting fitter and stronger — and then you get performances like this".
"I think that he made the difference higher up. I know he started off defending. But we wanted him to make runs in behind them, to get on the ball."
"His physical presence is important for us because we knew that Aston Villa are one of the strongest sides in the Premier League."