According to the Guardian's Fabrizio Romano and Ed Aarons, Sanchez has already agreed personal terms worth £250,000 per week with City, but United have now submitted a £25 million bid for the player and pledged to pay him a higher salary than the Sky Blues.
Sky Sport Italy's Gianluca Di Marzio corroborated the report:
Gianluca Di Marzio @DiMarzio
...#United in contact for #Sanchez in the last hours 😱@SkySport @SkySportNewsHD2018-1-11 12:08:23
Per Romano and Aarons, United's bid eclipses the £20 million offer City submitted for Sanchez earlier this week, and Red Devils manager Jose Mourinho is "confident of winning the race" to sign him, while Arsenal have been offered the chance to sign Henrikh Mkhitaryan.
The Armenia international has fallen out of favour with Mourinho in the last few months and failed to impress since a brief purple patch at the start of 2017-18—he has started just one Premier League match since Nov. 5.
The Independent's Miguel Delaney reported United are prepared to let him go and, based on Mkhitaryan's disappointing form during his time at Old Trafford, Sanchez would be a major upgrade as a replacement attacker.
The 29-year-old is capable of playing as a centre-forward, a No. 10 and on the left flank, and he has proved to be one of the Premier League's most effective attackers since joining Arsenal from Barcelona in 2014.
Sanchez would join a United attacking unit that already includes the likes of Romelu Lukaku, Anthony Martial, Marcus Rashford, Jesse Lingard and Juan Mata.
However, his chances of earning a regular starting spot would likely be better under Mourinho than City manager Pep Guardiola, who has an even larger abundance of quality forwards at his disposal.
City bid for Sanchez back in the summer, and it has seemed inevitable he would swap the Emirates Stadium for the Etihad Stadium for some time now, per James Olley in the Evening Standard.
United's interest has come somewhat out of the blue, but it makes a lot of sense.
Sanchez is potentially available for a relative bargain as he has only six months remaining on his Arsenal deal, he has proved his quality already in the Premier League and would be an upgrade on the disappointing Mkhitaryan.
Perhaps above all, though, United signing Sanchez would mean that City cannot—a potentially crucial point as the Red Devils try to make ground on their seemingly untouchable neighbours.