Retour
The Bluebirds triumphed 2-0 against the side two leagues below them in an FA Cup replay for the final qualifying round on Tuesday, October 20.
The alleged incident is believed to have happened after the full-time whistle with the player not yet named.
In a statement released on social media, a spokesperson for Gloucester City said: "Gloucester City AFC is appalled to have received reports of an alleged incident in which a Barrow AFC player was spat at following the full-time whistle during Tuesday evening's Emirates FA Cup fixture at the KMM Energy Stadium.
"The club strongly condemns any form of abusive, threatening or disrespectful behaviour towards players, officials or supporters.
"Such conduct is completely unacceptable and has no place at Gloucester City AFC."
Barrow AFC were forced into the 450-mile round trip following a 0-0 draw at the Furness Building Society Stadium on October 17.
In the subsequent replay, Kieran Thomas was sent off for the hosts before Thierry Latty-Fairweather hit his first goal for the Bluebirds, with substitute Arian Allen netting a stoppage-time second as Barrow went through at the second attempt.
The statement continued: "The club will thoroughly review all available footage to establish the circumstances surrounding the reported incident.
"Should any individuals be identified as responsible, appropriate disciplinary action will be taken, including stadium bans.
"Gloucester City AFC remains committed to ensuring a safe and respectful environment for everyone attending the KMM Energy Stadium."
The result on Tuesday evening means that Barrow AFC will be a part of the FA Cup First Round.
Another away trip beckons for fans as they face Gillingham at Priestfield Stadium on the weekend of November 7, with attention returning to league action in the meantime.