Sanchez is in the final six months of his contract at Arsenal and had been expected to move to United's local rivals Manchester City, after he almost joined Pep Guardiola's men at the start of the season.
The 36-year-old former Sweden worldwide suffered a horrific knee injury back in April 2017 in Manchester United's Europa League campaign and despite making an early comeback, he is yet to reach full fitness.
Manchester United manager Jose Mourinho has revealed that he is open to letting Henrikh Mkhitaryan leave this January should a club meet his asking price.
The fantastic opportunity for United to acquire Sanchez could be looming.
Mourinho admits winter is not a time in which he usually likes to do any business, unless circumstances dictate that purchases are necessary or a top player becomes available.
And, speaking during a recent interview, Mourinho refused to rule out selling the former Dortmund man in the current transfer window.
'And I am not the kind of blind manager.
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'My approach to players is that every player has a price - doesn't matter who he is, the level, doesn't matter the prestige, the status, every player has a price, ' said the United boss.
Nevertheless, Mourinho does not think that any signing will bridge the gap between United and City in terms of points in the Premier League this season, with Guardiola's side 15 clear ahead of their trip to Liverpool on Sunday.
"Blind in the sense that this player is untouchable, this one can never be sold". I think every player has a price.
Jose Mourinho has outlined both his, and the clubs transfer policy with regard to making signings in the January transfer window. Still, if the right player comes along, and at a steal of a price, you have to pull the trigger on executing the transfer buy.
"It's up to us to decide what we think is the right price".
Thursday's session was United's last at Nad Al Sheba Sports Complex following their arrival on Monday - three days after their FA Cup victory over Derby at Old Trafford.
'He is our player and a very good player. Vote in our match polls and have your say in the comments section below.