The Times says he has been on United's radar for a number of months, with the Red Devils making an enquiry about him last summer.
However, Aubameyang is hopeful of Barcelona formalising their interest in the coming weeks.
Mundo Deportivo says the Gabon forward would embrace the change of scenery and is hugely tempted by the prospect of playing at the Nou Camp.
The 31-year-old Gunners captain has just one year left on his deal at the Emirates and is understood to be seeking £250,000-a-week.
And he will reportedly only consider signing a new deal if no other teams contact him in the next few weeks.
Barca will move for Aubameyang if they cannot strike terms with Inter Milan for Lautaro Martinez.