Droylsden have begun an investigation with Chesterfield police into allegations of racist abuse towards Spireites defender Kevin Austin.
Saltergate stewards reported offensive noises allegedly aimed at Austin during Saturday's abandoned FA Cup second-round tie between the clubs.
Droylsden secretary Alan Slater said he had spoken to police on Tuesday.
"I raised the matter after we had a complaint. I asked them to help shed some light on it and investigate."
We do not tolerate any racial abuse and anyone caught racially abusing players, or other fans, will face arrest and prosecution
Chesterfield safety officer Colin Nellist
He added: "Our assistant manager of 15 years (Aeon Lattie) is black and Droylsden do not condone that type of behaviour.
"If it is proved to have happened then the club will take action."
Chesterfield have warned any repeat performance during the replay on Tuesday will be "swiftly dealt with".
Safety officer Colin Nellist said: "Due mainly to the conditions it was not possible to identify the perpetrators of what turned out to be an isolated but unpleasant incident.
"Our pledge is for Saltergate to be a welcoming place for everyone, so we do not tolerate any racial abuse and anyone caught racially abusing players, or other fans, will face arrest and prosecution."
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