Reports on Thursday [11 January] claimed Jose Mourinho is confident of beating rivals City to the signing of the Chile international with the club preparing a £25m offer.
City have been linked with a move for the out-of-contract Sanchez ever since failing to sign the 29-year-old from Arsenal on the final day of the summer transfer window.
Sanchez would be available to both City and United when the Champions League resumes in February and though the move may not affect the destination of the Premier League title, the deal could lay down a marker ahead of next season.
And former United defender Phil Neville, who won the league title six times while at Old Trafford, says the move would a massive "coup" for Mourinho's side and sent out a "strong statement" to their rivals.
"I was blown away really, because everyone thought he was going to the blue half of Manchester," Neville said in reaction to the speculation on a Sky Sports Facebook Live. "It's pretty obvious he's not going to stay at Arsenal. I think if United were going to buy him, £25m would be an absolute snip.
"United missed out on buying Ivan Perisic in the summer, and with that missed out on a winger. I think Sanchez provides the quality, the goals and the world-class ability he has got.
"I think it would be absolutely unbelievable signing. If you look back at Man Utd's big signings over the decades, Cantona came out of the hat, Van Persie was a surprise, and they both helped United win titles. I think this could have a similar impact. He's got the character to play at Old Trafford.
"It would be a coup, particularly for United fans, to have a player like Sanchez potentially come to them over City. It would be a strong statement."
With Sanchez having shown no interest in signing a new contract and remaining with Arsenal beyond the end of the current season, the north London club are running out of time if they want to command a fee for the forward.
They pulled the plug on Sanchez's departure in August due to being unable to line up a replacement and the same stipulation appears to be in place this month as Arsene Wenger bids to fill the void left by the former Barcelona forward.
The gamble of keeping Sanchez beyond the end of the summer window has not appeared to have paid off for Arsenal with the player having mustered just eight goals in 21 appearances which had come amid some lacklustre displays for the north Londoners.