The Portuguese claimed that appointing Taylor for the high-profile affair had put "pressure" on the official due to his links with the Manchester area.
Discussing referees prior to matches is forbidden, and Mourinho has now been contacted by the FA and given until 6pm on Friday to offer a response which will then be considered.
If found guilty of contravening the rule, which has been in place since 2009, the United boss is likely to face a large fine but avoid any sort of stadium ban.
Keith Hackett, the ex-head of the Professional Game Match Officials Ltd, was among those to criticise the decision to put Taylor in charge of the fixture, saying that "it would be intolerable" if there were a disputed call in the derby.
The game ultimately ended in disappointment, with an underwhelming goalless draw being played out in a match devoid of any real talking points.