Proposed by Enniskillen Town Councillor, Debbie Coyle, the motion asks that the Council "supports the same rights and entitlements to civil marriages for all citizens of Fermanagh regardless of race, religion or sexuality".
If passed, Fermanagh would be the fifth local authority across the Island of Ireland to endorse the Sinn Fein motion.
Belfast City Council was the first to support it last month, followed by Omagh, Magherafelt and Cork.
Although passed in each of these areas, the debates were not without their controversy.
In Omagh, one Unionist Councillor described gay marriage as a "gross sin" and an "abomination".
Continuing her party's aim to bring the matter to as many Councils as possible, Ms Coyle will open the motion up for debate in the Chamber during Monday night's full Council meeting.
"We are a party committed to equality for all the people," she told impartialreporter.com, "We feel it's important that every person, regardless of their race, religion or sexuality, have the same rights as heterosexual people.
"The move towards civil partnerships was a good step but it doesn't go far enough, especially in terms of issues concerning children and inheritance and that's why I'm hoping that people will support it.
"It's not for the State to discriminate against people over their sexuality. I'm hoping other Councillors see that and think it's important that all families, regardless of whether they are made up of heterosexual or same sex couples, have the same rights and equalities as everyone else."