Manchester United ejected a fan from the game with Liverpool for allegedly racially abusing a player who was reported to be Trent Alexander-Arnold.
The Old Trafford club say the fan will be banned for life if it is proved an offence was committed at Sunday’s game.
A United spokesman said the matter was being investigated “as a priority”.
A club statement added:
“Racism and all forms of discrimination are completely unacceptable and do not reflect the values of our club.”
“We are aware of an incident at yesterday’s game where an individual in the home section has allegedly engaged in racial abuse.
“The individual was identified and ejected from the stadium.”
Liverpool welcomed the “swiftness with which Manchester United have launched an investigation” and said the club would “support the strongest possible action being taken against anyone found to be responsible”.
United drew 1-1 with Liverpool to end the Premier League leaders’ 100% record.