A source said on Tuesday that Gueye did not play because he did not want to wear a rainbow-coloured number on his shirt.
The person spoke on condition of anonymity because Gueye has not commented publicly on the incident.
This is the second time Gueye has not appeared in a game wearing rainbow-coloured numbers after French football leagues did a similar event last May.
The federation’s ethics council sent Gueye a letter urging him to clarify why he missed Saturday’s game.
The council said if the reports are untrue the Senegal international could take a photo of himself wearing the jersey.
“Your absence has led to many speculations that have been very widely interpreted as a refusal to take part in this operation to raise awareness of the fight against discrimination,” council president Patrick Anton wrote.
Gueye travelled with his teammates to Montpellier for the game, but PSG coach Mauricio Pochettino cited “personal reasons” to justify Gueye’s absence from the field.
Anton wrote: "Either these suppositions are baseless, in which case we ask you to express yourself without delay in order to stop these rumours.
"We invite you, for example, to accompany your message with a photo of you wearing the jersey in question."
The letter carried on saying: "Or these rumours are true, in which case, we ask you to take stock of the impact of your actions and the very serious mistake committed.
"The fight against discrimination affecting different minorities is a vital and constant fight. Whether it’s skin colour, or religion, or sexual orientation, or any other differences, all discrimination is based on the same grounds — the rejection of others.
“By refusing to take part in this operation, you are validating discriminatory behaviour (and) the rejection of others, and not just against those in the LGBTQ+ movement.”
The case quickly became a political issue in both Senegal and France.
Senegalese President Macky Sall tweeted his support to Gueye.
Former Senegalese prime minister Abdoul Mbaye also threw his support behind Gueye, saying the PSG player “is not homophobic. He does not want his image to be used to promote homosexuality. Leave him alone.”
Homosexual relationships are considered a crime in Senegal and can be punished with up to five years in prison.