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."
The arrests come two weeks after the Football Association wrote to all clubs announcing that an anti-gay chant that has been used to target Chelsea players and supporters will be considered a breach of their rules.
The FA said those chants can have a "lasting and damaging impact" on people and communities within the game and must be stopped.
"This important step follows the recent successful prosecution of an individual by the Crown Prosecution Service for homophobic abuse, specifically relating to the term 'Rent Boy,'" the FA said.