City had been heavy favourites to sign the Chilean either this mornth or when his contract expires at the end of the season but were dealt a shock blow in their pursuit last week as arch-rivals United threw their hat into the ring.
With United prepared to offer Armenian playmaker Henrikh Mkhitaryan in part-exchange, a player Arsenal have known to be interested in in the past, the 'Red Devils' are now thought to be in the driving seat.
Sanchez was left out of the Arsenal squad for their defeat to Bournemouth at the Vitality Stadium on Saturday, with manager Arsene Wenger admitting that a decision on the player's future is imminent.
Today, English publication 'The Guardian' reports that City are set to pull out of the move over concerns that the financial package needed to complete the transfer is "excessive".
City had been reluctant to pay more than £20m for the 29-year-old this month and whilst there was some wiggle room with regard to that figure, the demands of Sanchez's agent Fernando Felicevich have scared off Pep Guardiola's side.
United boss Jose Mourinho fanned the flames recently as he admitted that United would delve into the transfer market this month for a "fantastic opportunity".