Manchester City are not prepared to pay more than £20million for a player that will be available on a free in the summer and United could swoop in with a £35million bid to hijack the deal.
Ryan Giggs, who made over 950 appearances for the Red Devils, spoke about Sanchez upon becoming the new Wales manager: "Whoever gets him, or whether he stays at Arsenal, they're lucky," Giggs said.
"He's not only a goalscorer, but he makes goals and works hard. So whoever gets him will be a lucky team because he is a top, top player.
"It doesn't happen very often where you're running down your contract, you've only got six months to go and you're able to get a player relatively cheap in this environment. But it is what it is, and like I said, whoever gets Alexis Sanchez will be extremely lucky."