The Chilean international has less than one year left on his contract at the Emirates and has decided against signing a new deal with Arsene Wenger's side as he seeks a move away from his current employers.
According to the Independent, Sanchez's intermediaries made contact with the Red Devils over a possible transfer and the report also goes on to claim that United manager Jose Mourinho's side would be interested in securing the player's services.
United's local rivals Manchester City, though, still maintain their interest in signing the 28-year-old. Despite his intermediaries approaching the Red Devils, a move to the Etihad remains the first choice for Sanchez.
After spending three years at Barcelona, Sanchez made a switch to the north London club in 2014. City's current manager Pep Guardiola signed the forward for the Catalan club in 2011 before stepping down from his position at Camp Nou a year later.
Sanchez scored 30 goals and registered 15 assists across all competitions as the Gunners finished the season with the FA Cup last term.
The Independent reports that Arsenal are still not looking to sanction Sanchez's sale in this transfer window. However, they could change their stance if a player is offered as a part of the swap deal.
It was earlier reported that City are willing to include Raheem Sterling in the deal, while the Gunners want Sergio Aguero.
There are also reports, however, that the City hierarchy don't want to lose either Aguero or Sterling, and are hopeful of completing a cash-only deal with Arsenal for the Chilean.
With the two clubs yet to reach any sort of agreement over Sanchez's transfer, United could take advantage of the situation and hijack City's move for forward.