Liverpool and Manchester United have urged fans to behave themselves during Monday's Premier League fixture at Anfield.
Both clubs were punished by Uefa over crowd disturbances at a Europa League last-16 game at Old Trafford in March.
On Thursday, a joint statement said supporters engaging in "offensive or discriminatory behaviour" risked prosecution.
"We ask all supporters to be respectful," they added.
Monday's match - which kicks off at 20:00 BST - will be the 197th fixture between the two clubs.
"This is an unrivalled fixture in the Premier League calendar and we thank all fans for their continued support in this important area of the game," the statement continued.
"If any supporters are found to be engaged in any form of offensive or discriminatory behaviour by stewards, or via CCTV, then they will be immediately removed from the stadium, risk arrest, prosecution and be reported in accordance with the club's ground regulations."
During the Europa League second-leg game last season, police made five arrests, after scuffles broke out in sections and some fans lit flares, while two United supporters were given community service orders over an "obscene" banner hung over the M602 motorway before the game.