The Football Association said it is looking into reports of chanting by Luton fans during the match with Liverpool that indirectly referenced the Hillsborough disaster.
The taunts were reportedly sung by some home fans during the second half of the Premier League match at Kenilworth Road, which ended in a 1-1 draw.
The FA said in a statement: "We are aware of tragedy chanting during the fixture between Luton Town and Liverpool.
"We are seeking observations from Luton Town and further detail from the Police.
"We strongly condemn chanting of this nature and will continue to work closely with our stakeholders across the game, including the clubs, leagues, fan groups, and the relevant authorities to proactively address the issue."
Bedfordshire Police said it is "in talks" with Luton Town.
After the match, Reds boss Jurgen Klopp said he did not hear the chanting, which occurred while the game was still goalless shortly after half-time, but added: “Shame on everyone who said it.”
It is believed the chanting indirectly referenced the tragedy on 15 April 1989 - when 97 football fans died at Hillsborough in Sheffield due to a crush at an FA Cup semi-final match between Liverpool and Nottingham Forest.
Former Reds defender Jamie Carragher, who was commentating on the game for Sky Sports, said: “As supporters you’ve got to have rivalry, there is no doubt. But we’re better than that.
“It’s happened two or three times in the game. All clubs have been guilty of that over the years at different times.
“But the world we live in right now, I think we’re better than that.”
In June, a man who wore a shirt at last season’s FA Cup final which referenced the Hillsborough tragedy was issued with a four-year football banning order.
The Football Association has since imposed tougher rules for tragedy-related offences, including stadium bans and potential criminal prosecution.
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To know...