Three men were arrested following reports of alleged homophobic chanting at the goalless draw between Liverpool and Chelsea at Anfield, Merseyside Police said on Tuesday.
The men, aged 23, 37 and 49, were arrested on suspicion of homophobic intentional harassment alarm and distress in Saturday's game, the police said in a statement to Reuters.
In three separate incidents, two arrests took place outside the stadium on Anfield Road and one inside the ground, it added.
"Merseyside Police will not tolerate hate crime of any form, and we will bring to justice anyone found responsible for committing any offensive chanting," said Superintendent Paul Sutcliffe and match commander for the game.
"In this instance, if the three suspects are charged and found guilty for the offence, then we will we will be seeking football banning orders on them."