The forward is in the final year of his contract at Arsenal and has rejected all offers to sign a new deal.
He was pursued by Manchester City in the summer transfer window but they were unsuccessful with a £60million bid after Arsenal failed to land a replacement ahead of the deadline.
City are expected to make a fresh attempt to prise the 28-year-old to the Etihad in January when the transfer window re-opens.
But, according to The Sun, they now face competition from bitter rivals United.
Jose Mourinho is said to be eager to add to his attacking options and is targeting a deal for the former Barcelona star next summer
Sanchez will be available on a free transfer then but United will have to pay a signing-on fee of around £25million to secure his signature.