Liverpool say tragedy chanting "has to stop" after songs related to the Hillsborough disaster were sung by some Chelsea fans during Tuesday's 0-0 Premier League draw at Stamford Bridge.
Chelsea apologised and condemned the "inappropriate" chants saying "hateful chanting has no place in football".
The Premier League says such chanting is "an unacceptable issue and are seeking to address it as a priority".
This season has seen a rise in tragedy chanting.
Manchester City said they were "disappointed" by "inappropriate chants" by their fans during Saturday's 4-1 win over Liverpool.
Last month, Liverpool and Manchester United managers Jurgen Klopp and Erik ten Hag called for an end to tragedy chanting in a joint statement before the two sides met.