The Frenchman is still determined to force his way out of the club after several attempts to leave last summer failed
Juventus and Real Madrid are keen to land 24-year-old who is yet to feature for the Red Devils since September 30, because of a foot injury.
Pogba, who was expected to return in action this week was hit by a mystery illness.
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Solskjaer told his pre-match press conference ahead of Manchester United Premier League clash with Everton on Sunday: “He’s [Pogba] not getting sold in January, no.
“He’s training but he’s not been training with us for long. He’s training and that’s a step forward for us.
“Yeah, of course (I understand all the interest around him) because he’s a fantastic player, a charismatic personality and for us we’re happy that he’s here.
“When he comes back, play well, play with a smile on his face and do what he did a year ago when I came here,” Solskjaer added.
“Paul was fantastic. He has been fantastic when he’s played for us.
“We know that we’ve got one of the best players in the world when he’s playing well, when he gets fit.
“He needs time to get fit of course but he’ll make a difference for us.”