The Dutch ace only joined the Red Devils from Arsenal in 2012, and immediately fired them to Premier League glory last season.
However, he is rumoured to be unsettled following the arrival of David Moyes as manager this term.
RVP was known to have a good relationship with Sir Alex Ferguson – who played a major role in luring him to the club – and was left upset when the Scot elected to retire over the summer.
The 30-year-old is also said to be unconvinced by Moyes’ training methods and tactical approach, which he openly questioned after Tuesday’s Champions League defeat at the hands of Olympiakos.
Arsenal are thought to be interested in bringing back their former captain, with Arsene Wenger seeing him as the solution to his striking concerns despite some fans having not forgiven him for his decision to quit the club in the first place.
Van Persie still has two-and-a-half years on his contract, but United may be tempted to sell as they look to rebuild their squad in a bid to improve on-field performances.