Jose Mourinho’s club reached out yesterday to the Gunners, testing the water over whether they would be willing to accept £25million for the Chile forward.
That is more than the £20m City are believed to be prepared to pay for Sanchez, who can move on a free transfer this summer when his contract with Arsenal expires.
United also tabled the possibility of midfielder Henrikh Mkhitaryan moving to the Emirates as a makeweight in the deal as Mourinho looks to offload the Armenian in this transfer window.
And United are hoping their superior offer tempts Arsenal into agreeing to sell him this month.
In addition, sources claim United are offering a higher basic contract to Sanchez than the £250,000 a week he is believed to have accepted, in principle, when he almost joined City on the final day of the last transfer window in the summer.
Arsenal are privately resigned to losing Sanchez and the only issue remains whether they allow him to leave now or keep him until the summer and lose him for nothing.
The Gunners are looking for a reported £35m to do business now and the United package is far closer to that demand.
But the general belief, both at Old Trafford and the Emirates, remains that City are strong favourites to land Sanchez due to the player’s past relationship with Guardiola, for whom he played at Barcelona.
So confident are City of landing their man they had been relaxed about the need to move for him over the first half of the season, in which they have yet to lose to an English team in any competition.
Brazilian striker Gabriel Jesus, however, could be out for two months with a recent knee ligament injury and veteran record scorer Sergio Aguero remains the only orthodox centre-forward in City’s squad.
United will be back on live television in the FA Cup after their fourth-round tie with Yeovil later this month was selected for coverage.
Yeovil, 21st in League Two, are the lowest-ranked side remaining in the competition and United’s trip to Huish Park has been moved to a Friday night and will kick-off the fourth-round action on January 26 live on BBC One.
It comes after United’s game with Derby in the previous round was also held on a Friday night but not broadcast live, ending the Red Devils’ extraordinary run of 58 consecutive televised FA Cup ties stretching back 13 years.
Saturday, January 27 sees a triple-header on BT Sport as Peterborough host the winners of next week’s replay between Leicester and Fleetwood in a 12:30pm kick-off, while Newport’s reward for their win against Leeds sees their home tie with Tottenham screened at 5:30pm.
The all-Premier League clash between Liverpool and West Brom is scheduled for 7:45pm and this will be the first time that the Football Association has used that slot to show a live FA Cup game.
The coverage will continue on BT Sport on January 28 as the winners of the replay between Chelsea and Norwich host Newcastle in a 1:30pm start, while later that Sunday Premier League leaders Manchester City will be on BBC One at 4pm at either Cardiff or Mansfield.