The real-life couple - who play bickering exes Tammy and Ron on the NBC show - will take on the role of parents, Variety reports.
Gay Dude centres on two boys named Michael and Matty who promise each other they will have sex before their senior prom.
However, Matty then reveals that he is gay to Michael, making their mission slightly more complicated.
Offerman will play Michael's supportive father, who believes his son is gay after finding him Googling 'gay', while Mullally and Gary Cole star as Matty's conservative parents.
Nicholas Braun and Hunter Cope are to star as Michael and Matty respectively, with The Social Network's Dakota Johnson and The Sitter's Dreama Walker in supporting roles.
Braun will next be seen in Kevin Smith's controversial film Red State.
Offerman recently revealed that Mullally had coached him through numerous auditions before he landed his ideal role in Parks and Recreation.
Watch the red band trailer for Red State below: