Saacute;nchez has already agreed personal terms worth around pound;250,000 a week with Pep Guardiola's side, with City having submitted a pound;20m offer for the 29-year-old earlier this week. Arsenal have yet to respond to that but it is understood that United have since entered the race with a bid that is believed to be in the region of pound;25m.
Their proposal would also see Saacute;nchez earn more than he has been offered by City, with Mourinho believed to be confident of winning the race despite the forward having played under Guardiola at Barcelona.
Arsenal have also been offered the opportunity to sign Mkhitaryan, although a stumbling block to that deal could be the Armeniainternational's wages, which are believed to be around pound;200,000 a week.
Arsegrave;ne Wenger is keen on signing Malcom from Bordeaux as a direct replacement for Saacute;nchez and has held preliminary talks with his agent this week. The Brazilian forward is understood to have another firm proposal to leave this month, although it is understood not to have come from either United or Tottenham, who have both been linked with the 20-year-old in recent weeks.