"He has until 6pm (1800 GMT) on Monday 18 December to respond," an FA spokesperson said on Twitter.
In his final pre-game press conference, Mourinho suggested City's players were prone to diving, saying it only takes a "little bit of wind" for them to go to ground.
He also questioned City manager Pep Guardiola's right to wear a ribbon in solidarity with jailed Catalan separatists, suggesting it was something he "wouldn't be allowed to do".
The FA is already investigating a mass brawl that allegedly erupted after Sunday's game at Old Trafford, which was reportedly instigated by Mourinho's complaints about the noise of City's celebrations.
The two clubs have been given until Friday to provide observations about the incident.
United's defeat left them 11 points below Premier League leaders City in second place.
Mourinho's side beat Bournemouth 1-0 on Wednesday and visit West Bromwich Albion on Sunday.
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