Fun Home is based on the book of the same name by illustrator Alison Bechdel, a memoir recounting Bechdel's life from childhood to present day in which she discovers her own sexuality and attempts to make sense of her relationship with her closeted gay father.
The stage adaption features a book and lyrics from Lisa Kron with music from Jeanine Tesori.
The show made its debut Off-Broadway in 2013 before transferring to Broadway in 2015 where it went on to win five Tony Awards, including Best Musical.
Fun Home made its London premiere at the Young Vic in 2018, receiving Olivier Award nominations for Best New Musical, Best Actor and Outstanding Achievement in Music.
According to the Daily Mail, Jake Gyllenhaal is working on a film adaption that would see him play Bruce Bechdel, Alison's father.
Sam Gold, who directed the show in both New York and London, is attached to direct with further casting and details to be confirmed.
In the mean time, Gyllenhaal is set to star in Sunday In The Park in London's West End from May.