The 28-year-old is looking to leave the Gunners and has refused to commit his future to the club.
Manchester City have been looking to secure a deal for Sanchez this summer.
Pep Guardiola has even offered Raheem Sterling as part of an exchange deal for the Arsenal star.
But the prospect of a move to Old Trafford appears to be a possibility too ahead of Thursday's 11pm deadline.
According to The Independent, Sanchez is now 'desperate' to leave the Emirates in this window.
He no longer seems prepared to stay and play out his final season at Arsenal.
And that urge to leave has apparently seen intermediaries get in contact with United to see if they are interested.
The Independent add Jose Mourinho would want Sanchez.
However, the player's first choice remains a move to City due to his relationship with Guardiola.
Arsene Wenger does not want to lose Sanchez but Arsenal could be more open to a departure if they get someone in return.
City are said to be reluctant to lose either Sterling or Sergio Aguero in a deal for Sanchez.
And it remains to be seen if United will make a late move for the Arsenal ace.
Meanwhile, Sanchez has asked for permission to leave Chile's training camp while his future is sorted.
