The Danish international is ready for a "new challenge" with only one year left on his contract in north London.
And that could come at Old Trafford according to the Sunday Mirror.
Juventus are also an option being considered but Real Madrid appear to have moved on to other targets.
The move for Eden Hazard appears to have ended any chance of Eriksen moving to the Bernabeu this summer.
United's move to add a defender this summer is edging closer with the club and Crystal Palace close to an agreement over a fee for Aaron Wan-Bissaka.
The Old Trafford club had initially been hoping to prise the 22-year-old from Selhurst Park for £25m, but Palace have been steadfast in their stance.
However, the Daily Mail report that after lengthy discussions a fee of around £42.5m plus add ons has been agreed to finally get a deal done.
Ole Gunnar Solskjaer sees the 21-year-old as key to the rebuild of his squad this summer.
Meanwhile United have upped their interest in Sporting midfielder Bruno Fernandes and want him on board in time for pre-season.
The Portuguese international is set leave this summer after a record-breaking season in his homeland with some of Europe's top clubs lining up to sign him.
Tottenham, Liverpool and Paris Saint-Germain have all been credited with interest in recent weeks.
But Record report it's United who lead the race suggesting that the 24-year-old is "most likely" to end up at Old Trafford.
Meanwhile, West Ham want Anthony Martial in exchange for Issa Diop, if any deal is to be done for the centre-half.
The Old Trafford hierarchy have investigated the possibility of signing the 22-year-old, but West Ham have so far shown no willingness to sell.
In initial talks, however, the London club have indicated that they may be willing to do business if Martial comes the other way.
In better news United now believe that David De Gea will sign a new deal with the club.
That's according to The Sun.
They say the Spanish international is set to pen a new contract worth upwards of £350,000 a week.
Pogba has finally made his desire to leave Old Trafford clear, stating that it’s time for a “new challenge”, but many sources say he’s for a long time been “desperate to leave”.
Zinedine Zidane wants Pogba to join Real Madrid at any price, but the Bernabeu hierarchy are not keen to spend more than £110m after a summer that has already seen them break £350m.
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