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The France international is out of contract in July and able to negotiate with Europe's top clubs right now.
Real Madrid are long-time admirers of Pogba, while Paris Saint-Germain and former club Juventus have registered an interest.
SunSport report United are desperate to keep their record signing and want to make him the highest-paid player in Premier League history.
The 28-year-old is set to earn a basic wage of £400,000-per-week which would then rise to £500,000-per-week with add-ons.
United are aware Pogba would net a massive signing-on fee should he choose to leave Old Trafford at the end of this season but are refusing to sell in January.
Pogba is currently out with a hamstring injury and his last appearance came during November's 2-2 draw with Atalanta in the Champions League.
His last Premier League start dates back to October, when he was sent off for a challenge on Naby Keita in 5-0 defeat to Liverpool.
This season saw Pogba register seven assists in his opening four games but then tail off before getting injured.
Since then, Ole Gunnar Solskjaer has been sacked and the Red Devils have appointed Ralf Rangnick as interim manager.
Monday saw United slip to a 1-0 defeat to Wolves and it was their first win at the Theatre of Dreams since 1980.
The Daily Mail have claimed up to 17 players are unhappy at United and the mood around Carrington is at breaking point.
Rangnick is in charge until the end of this season and he's believed to have admitted that fixing the problems in just six months isn't possible.
Defender Luke Shaw gave an explosive interview earlier in the week and hinted at dressing room unrest.
Shaw told Sky Sports while analysing the Wolves clash: "We have to put more pressure on them, we have to have intensity.
"Us players, we have been here a long time, maybe tonight we struggled, I didn't think we were all there together. You look at the players we have, we have unbelievable quality but sometimes quality is not enough.
"We need to bring the intensity and more motivation. Inside the dressing room, we know what we want but out on the pitch we need to give 100 per cent.
"To win these types of games we all need to be 100 per cent committed. It is tough and disappointing."
United sit seventh in the league, four points behind Arsenal in fourth.
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