Earlier this season, the Frenchman fell out with former United manager Jose Mourinho, who allegedly called him a ‘virus’ during a dressing room rant.
Solskjaer has been able to get Pogba firing again since replacing Mourinho as manager in December, but he has not scored or assisted a goal in his past six games.
French outlet Le Parisien claim Pogba’s relationship with Solskjaer is ‘slowly fading’ amid reported interest in the France international from Real Madrid.
The 26-year-old admitted last month that a move to the Bernabeu would be a ‘dream’, especially now Zinedine Zidane has returned as Los Blancos’ manager.
But Solskjaer has tipped his star midfielder to stay at Old Trafford beyond the summer.
LIVE ON talkSPORT
talkSPORT is your home of live football! Here's what's coming up on talkSPORT and talkSPORT 2…
- Slavia Prague vs Chelsea (Thursday, 8pm) – talkSPORT 2
- Southampton vs Wolves (Saturday, 3pm) – talkSPORT 2
- Manchester United vs West Ham (Saturday, 5:30pm) – talkSPORT
- Leeds vs Sheffield Wednesday (Saturday, 5:30pm) – talkSPORT 2
- Wigan vs Norwich (Sunday, 12pm) – talkSPORT 2
- Crystal Palace vs Manchester City (Sunday, 2:05pm) – talkSPORT
Prior to Manchester United’s 1-0 defeat to Barcelona in the first leg of their Champions League quarter-final, he said: “Paul is looking forward to tomorrow. He’s a Manchester United player.
“He’s one of our, of course, big performers on the big stage.
“He knows the game against PSG [when Pogba was sent off] was not his greatest moment so he is only focused on playing well tomorrow against Barcelona.
“I cannot see him not playing for Man United next season either.”
Pogba’s threat was minimised by experienced Barcelona midfielder Sergio Busquets on Wednesday night.
The United star will be hoping for better luck when his side travel to the Nou Camp next Tuesday.