Guardiola was booked during the game for angrily remonstrating with the officials after they did not show James Milner a second yellow card for a foulManchester City have made a complaint to Liverpool after alleging a home fan spat at their backroom staff in the first-half of the 2-2 draw at Anfield.
Manager Pep Guardiola said he was not aware of the incident at the time but was subsequently notified.
"They [the staff] told me but I didn't see it," he said after the game, which saw his side come from behind to draw.
"I'm pretty sure Liverpool FC will take measures against this person. I know they are greater than this behaviour."
It is understood Liverpool are investigating the incident and are looking at CCTV footage from that area of the ground.
In a thrilling game on Merseyside, City twice came from behind to claim a point, with Kevin de Bruyne levelling the second time after Mohamed Salah's superb solo goal had put the Reds ahead.
It was not without on-field controversy, though, with Guardiola furiously remonstrating with the officials for what he felt should have been a second yellow card and dismissal for Liverpool full-back James Milner.
Milner's foul on Bernardo Silva just before Salah's goal went unpunished, with Guardiola himself later booked for his protests.
The draw leaves City third in the table on 14 points, a point and a place worse off than Liverpool and two points behind leaders Chelsea.
