United are willing to pay the Gunners £25m plus Mkhitaryan to land Chilean winger Sanchez.
And the potential exchange deal has taken another step towards to completion.
The BBC claim Mkhitaryan’s ex-club Dortmund made an enquiry.
But they have decided not to pursue the 28-year-old anymore because they feel United’s asking price was excessive.
The Bundesliga giants have reportedly ruled out making a bid to bring him back to Germany this month despite doing so with several stars in the past.
Dortmund has re-signed Shinji Kagawa from United and Mario Gotze from Bayern Munich in recent years.
But the BBC reported they will not be bidding for Mkhitaryan this month, seemingly leaving him clear to swap clubs with Sanchez.
United legend Gary Neville believes it is a no-brainer for Jose Mourinho to replace Mkhitaryan with Sanchez.
He told Sky Sports: “The clearest sign that something’s happening with Sanchez is that Mkhitaryan isn’t playing, that he’s not in the squad and Jose was happy to volunteer that information to us.
“He wanted to keep the player clear, saying that he does rate him but I think he’d happily swap him in any deal for Alexis Sanchez. Anybody would.”
Asked if he’s been convinced by the Armenian, Neville added: “Not fully.
“He’s a talented player but you have to have more than talent. He’s shown glimpses that make you think he’s coming but then he goes missing.”
