The teams said they are committed to dealing with unacceptable behaviors.
In November, the clubs and their fan groups held a meeting and made a commitment to improve relations.
Two sides sent a letter to supporters asking them to report any incidents that cause harm.
They are going to play in the fourth round of the Carabao Cup.
The passion and enthusiasm that we see from our fans when we play each other is part of what makes matches between our clubs so special.
You are committed to creating a stadium environment where everyone is accepted and has a great match day experience.
A minority of fans are responsible for the actions that have no place in our game.
To ensure that both of our clubs' good names are preserved, we are asking for your full support in tackling these behaviors.
The last time the two teams met in the league, it was at home where the Reds won.
The City boss said members of the crowd at the other side threw coins at him.
The Manchester club were unhappy with the comments made by the Reds boss about their spending power, as well as the damage to their bus, which they claimed was caused by a broken window.
The coach of the City team was attacked prior to the game against the Reds in April of last year.
"You can help us by reporting any incidents so we can investigate them," the letter continued.
Some fans may not be aware of the impact of their behaviors on other fans, and we will continue to work with our fans on this education.
We are committed to dealing with unacceptable behaviors and will take action by issuing bans to those found to be responsible.
We can all concentrate on supporting our teams if we all report the actions that cause harm, such as inappropriate gestures, chanting, throwing of objects, and discrimination.
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