The club revealed they have received 'numerous complaints', all from their own supporters, alleging racist chanting from a section of Vale fans in the Railway Paddock towards the visiting supporters.
The Football Association has been informed and the Staffordshire club are appealing to fans with information to contact Port vale.
A statement on the Port Vale website read: "Port Vale is bitterly disappointed to receive a number of complaints of alleged racist chanting from home supporters in the Railway Paddock towards the visiting Bradford City supporters on Saturday.
"As well as numerous complaints to the club, all from Port Vale fans, a complaint has also been raised directly by a home supporter with 'Kick It Out', football's equality and inclusion campaign.
"In turn, this has now been escalated to the Football Association.
"Port Vale does not tolerate mindless behaviour of any kind and any supporter who is found to be partaking in abusive or discriminatory behaviour of a racist nature faces a life ban from Vale Park, as well as the possibility of criminal proceedings.
"These allegations tarnish not only the good name of Port Vale Football Club, but also the thousands of Valiants supporters, including families and children, who attend home games with no issues.
"Port Vale would strongly urge supporters who enjoy taking part in racially motivated abuse not to attend games. You are not welcome at Vale Park.
"If you have any information relating to Saturday's alleged chants, please contact the club. Any information will be treated in the strictest of confidence."