Liverpool and Manchester United have issued a joint statement ahead of Monday's game at Anfield to warn fans they could be ejected or prosecuted for any "offensive or discriminatory behaviour."
In May, both clubs were fined €40,000 (£30,565) by UEFA, half of that suspended for a probationary period of two years, after crowd disturbances and "illicit chanting" during a two-leg Europa Cup clash last season.
Liverpool were fined a further €17,000 after supporters set off fireworks and threw objects and the first leg at Anfield kicked off late.
United, meanwhile, had to pay an additional €18,000 over crowd disturbances, blocked stairways and the throwing of objects.
The joint statement said: "Both clubs, their supporters and football fans around the world are looking forward to this historic and passionate match between two of the sport's biggest and oldest rivals.
"There is great rivalry between our fans, and we ask all supporters to be respectful and help eradicate all forms of offensive and discriminatory behaviour from the game.
"If any supporters are found to be engaged in any form of offensive or discriminatory behaviour by stewards or via CCTV, they will be immediately removed from the stadium, risk arrest, prosecution and be reported in accordance with the club's ground regulations.
"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."
A spokesperson for anti-discrimination group Kick it Out, said the two clubs "should be commended for this proactive approach ahead of this important fixture."
The spokesperson said: "We always encourage supporters to report any form of discrimination they may see or hear.
"Our reporting app, which is available to download from the App Store and Google Play, allows users the option to attach photos and videos."