The Championship side's chief executive and former player and manager Gerry Britton issued a statement on the club's website.
Thistle fans usually sing the song in reference to Celtic and Rangers but have recentlybeen reported to the SPFL by league delegates.
The statement said: "Partick Thistle is a family club and aim to ensure that everyone experiences a friendly and safe atmosphere at our games.
"We are aware that a minority of our supporters are singing a song that is deemed to be unacceptable by the footballing authorities.
"This behaviour has been included in recent SPFL match delegate’s reports and continuation of this conduct may lead to the club being punished.
"Consequently, we appeal for this type of singing and chanting to stop and request that supporters refrain from engaging in any form of behaviour that is unacceptable, disrespectful and which others may find offensive.
"Partick Thistle is extremely proud of our support and don’t want anything to damage our reputation. Your cooperation is appreciated."