The Premier League leaders have made a £20m offer for the Chile international after seeing their attempts to sign him last summer fall through on transfer deadline.
Sanchez is understood to be eager to link up with Pep Guardiola - whom he worked under at Barcelona - once again at the Etihad Stadium.
But latest reports now suggest City are not ready to increase their offer for a player who has less than six months left on his contract, with Arsenal thought to be holding out for £35m. The player's agent, Fernando Felicevich, is also demanding a fee of £5m for his part in negotiating the deal.
The Daily Mirror claim City are also not prepared to agree to the financial package put forward by Sanchez's representatives, with the player's wage demands thought to be £300,000-per-week. City will end their interest unless Sanchez's camp lower those demands.
Their stance leaves United with a free run at the former Barcelona and Udinese star if he remains intent on leaving north London this month.
On Thursday [11 January], it emerged United had entered the fray with an offer of £25m, with the club prepared to offer Sanchez a more lucrative financial package than the one put forward by City.
The Guardian added that Mourinho is confident of getting the deal wrapped and beating his old rival Guardiola to what would be one of the biggest transfers of the mid-season window.
To sweeten the deal, United have also offered Arsenal the chance to sign Henrikh Mkhitaryan, with the Armenia international out of favour under Mourinho at Old Trafford. Wages could be an issue, however, with Mkhitaryan, who was strongly linked with a move to north London before arriving in Manchester, reportedly earning around £200,000 on a deal he signed upon his arrival at the club just 18 months ago.