The Brazilian, who can play wide right or left, is an outstanding technical player though Arsenal recognise he will take time to adapt to the physicality of the Premier League.
However, according to the Independent, United could also move for Sanchez's Arsenal team mate, Mesut Ozil.
"His situation is not decided one way or the other so I left him at home", he said.
Manchester City had been regarded as the favourites to sign the 29-year-old forward this month, but senior figures at the Etihad told ESPN FC on Friday that the Premier League leaders would not pursue a move for the Chilean unless Arsenal substantially dropped their £35m asking price for a player with less than six months remaining on his contract.
"At the moment their need is perhaps less than Jose Mourinho's need and that probably shows you why Manchester United are so keen on bringing Alexis Sanchez to Old Trafford".
"I look at Arsenal without Sanchez and Ozil and I'd ask what name would fans get on their shirts if those two go?"
United have a lot of creative players in the final third, but none is as influential as Sanchez.
It is hard to envisage Sanchez staying beyond January, but Arsenal will not sell him unless they can bring in a replacement, with a £35m bid for 20-year-old Malcom expected this week.