Sanchez, 28, was on the verge of securing a deadline day move to Manchester City after Arsenal accepted a bid totalling £60million.
However, Arsene Wenger blocked his move to the Etihad after failing to land Monaco winger Thomas Lemar as his replacement, with the France international opting against a switch despite the Ligue 1 champions accepting the offer.
The Chile international looks destined to leave Arsenal on a free transfer after refusing to sign a contract extension.
Sanchez is demanding around £400,000-a-week, which Manchester City are reportedly willing to pay him.
Pep Guardiola is keen on securing a reunion with him and could reignite his interest in the former Barcelona man in January.
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But The Sun claim Manchester United boss Jose Mourinho is keen on hijacking his move to rivals City.
It is said that the Portuguese boss has been quoted a £25million signing-on fee for Alexis Sanchez.
However, he will be unable to sign a pre-contract with United until the new year.
But an agreement in principle could be put in place for the deal to go through next summer.
Arsenal host Doncaster in the Carabao Cup tonight (7:45pm) and Sanchez is likely to play a part.
While United take on Burton Albion at Old Trafford (8:00pm).