The newly formed 1887 Red Army were seen to react angrily during the League Two fixture on Saturday after chants were aimed towards them from certain sets of away supporters.
However, it appears that the abusive chants had began outside of the Jonny-Rocks Stadium ahead of kick-off.
Speaking about the claims, The Robins’ media manager Richard Joyce said: “I didn’t hear anything myself.
“We have not really been communicated anything but I think there is communications going on with the police in regards to things that may have happened outside the ground.”
Port Vale have previously teamed up with local police to bring a zero tolerance outlook on racism, warning fans that they will be taken to court and handed lengthy bans if any racial chants were heard.
However, it is important to note that no racism has been confirmed at the game on the weekend.
“I don’t know anything about inside the ground but that is something that we will have a talk about and see if anything has to be done”, said Joyce.
“But as of yet we have not had anything official complaint made to us in regards to what has happened.”
Despite the potential of racism overshadowing the fixture, the two sides fought in a battling game that ended level.
However, Joyce remained upbeat that Cheltenham Town can finish in a promotion play-off position.
“We are six unbeaten after Saturday.
“It wasn’t the best performance but I think it was important that we didn’t lose the game against another one of the leading teams in the division”, he said.
The Robins remain ahead of Port Vale in fifth and will now look towards a tricky away fixture against Cambridge United on Saturday.