Mourinho said appointing Taylor for the game had put “pressure” on the Manchester-based official.
Managers are not supposed to speak about referees prior to matches.
The Portuguese, 53, has until Friday to offer a response, which will then be considered by the FA.
Monday’s game finished 0-0.
Former referee Howard Webb told BBC Radio 5 live that Mourinho should be “taken to task” by the FA.
“It’s one thing someone from Manchester or Liverpool taking to social media, a fan commenting, but for a coach to do this when he knows the rules then there should be some action taken against him,” added Webb.
“Focusing the attention on a referee is simply mind games and trying to gain an advantage.”
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