According to Neil Custis of The Sun, the Red Devils want to capitalise on the former Barcelona man's contract situation, with his current deal set to expire at the end of the Premier League season. However, James Olley of the Evening Standard reported City are still favourites to land Sanchez.
It's suggested in the report that Sanchez would be able to command a signing-on fee of £25 million if he left Arsenal and became a free agent. City were ready to pay around £60 million for the Chile international in the previous transfer window.
However, Sanchez remained at the Emirates Stadium and looks poised to see out his Arsenal contract.
The desire from Arsenal to keep the South American is understandable, as he's one of the most dangerous footballers in the Premier League. Last term he was a regular scorer of goals and creator of chances for the team, bringing an incision and inventiveness to the Gunners' play.
After a summer of international commitments and transfer speculation, the forward has been eased back into Arsenal's 2017-18 plans.
Journalist Tom Victor joked about his involvement so far:
Tom Victor @tomvictor
Big fan of Wenger using Alexis as a league sub and cup starter like he's a South American Gervinho2017-9-17 12:40:38
According to Custis, some associated with City were "surprised" that manager Pep Guardiola was so keen to sign Sanchez.
After all, it's in attack where the Etihad Stadium outfit are strongest. Sergio Aguero remains one of the most feared strikers in the Premier League, while a supporting cast of Gabriel Jesus, Raheem Sterling, Leroy Sane and Bernardo Silva make this City team so good in the final third.
Per Sky Sports News' Kaveh Solhekol, City are ready to move for the player again in January instead of waiting until the end of the season:
Kaveh Solhekol @SkyKaveh
Man City have not given up on signing Alexis Sanchez. Will try to sign him again in January. Will cost much less than yesterday's £60m bid2017-9-1 18:45:29
Interest in the Chilean from United, or any other elite side in European football, would also make sense.
The Red Devils have also started the season with an attacking swagger, with Romelu Lukaku bringing goals. However, the addition of another world-class option to play on either flank or in support of the Belgian would give the team an added dimension.
Sanchez's industrious and intricate style would be a perfect fit for the manner in which United manager Jose Mourinho wants his team to play.
Having clung on to Sanchez all summer, it would be a shock to see Arsenal sell in January. As noted by football writer Daniel Storey, he's vital to the team:
Daniel Storey @danielstorey85
Since Alexis Sanchez joined Arsenal, they have never won a Premier League game in which neither him nor Mesut Ozil started.2017-9-17 11:59:37
From the player's perspective, being a free agent would see him benefit financially, especially if he were able to command such a lucrative signing-on fee.
Given they pursued Sanchez throughout the summer and the player has worked with Guardiola previously, City surely remain favourites to bring in the Arsenal man.
If United were able to pull off a deal, though, it would be a huge boost, not just in terms of securing a world-class talent but also snatching him from under the noses of their neighbours.