Manchester United have texted their fans before the game at Liverpool to tell them any "racist or discriminatory behaviour is unacceptable".
Police are investigating the alleged racial abuse of Manchester City forward Raheem Sterling at Chelsea last week.
Some Chelsea fans were also accused of singing an anti-Semitic chant in a Europa League game in midweek.
United said they wanted fans going to the game at Anfield "to support the team in a passionate and positive way".
Their message added: "After recent incidents at other clubs (and in line with our own long-standing policies), we're joining the Premier League in reminding supporters that any kind of racist or discriminatory behaviour is unacceptable and has no place in the game.
"As a club that has suffered tragedy in the past, the same applies to songs that reference tragic events that have affected other clubs."
Manchester United and Liverpool fans have previously directed chants at each other relating to tragedies involving the two clubs.
In 1958, eight United players were among 23 people who died after their plane crashed on take-off in Munich.
The Hillsborough tragedy saw 96 Liverpool fans die at an FA Cup semi-final tie with Nottingham Forest in 1989.
SINGAM23
2
Fans and Supporters knows what is best for their favorite club...
Pebiklorz
2
liverpool win this match😍😍😍😍😍😍😍
Stellen_Henriques
2
again & again fans are spoiling the beauty, I'm tired of this
please stop it for Gods atleast
BlueShinjuku
0
Yes we don't need those useless racist fans to give us headaches like the one Chelsea is having now
definitely, it doesn’t make the team look good at all, and it gives the club have problems like fines. totally unnecessary to be racist or rude to other fans. support a team without hate speech.
Alakiri
4
this game is game of the generals
reached
2
I must ARCHIVE this and show it to my GRAND KIDS, DECADES TO COME. EXCITED!!!!!
educate
3
2-1 for United let's go boys👏💪💪❤
12UnitedGuyReborn
3
Yes we don't need those useless racist fans to give us headaches like the one Chelsea is having now
vamosl
2
Manchester United fans
RichardAllen
0
Pogba slows the game and is a defensive liability against pressing teams. Toss up between Mata and Lingard although Lingard offers a little more pace in the middle and Martial is coming off a groin injury so can’t play 90 minutes yet. Expect him off the bench.
Peterjerry
3
Liverpool will show them who is in charge
moore8
2
Prevention is better than cure,the only way you can prevent is by passing out information even when it’s very well known by everyone,thanks United for the alert created and hope the fans obey as usual
Kingkley
0
Win today or I won't let my grandma out.