He is the frontrunner to helm the adaptation of the musical that charts the career of Frankie Valli and The Four Seasons, according to Variety.
Hugo producer Graham King has been pursuing the project for several years now, with the latest report indicating that it is close to receiving the green light.
The film will use much of the same songs and lyrics as the show, which debuted on Broadway in 2005 before going global.
Favreau has most recently been focusing on comic book action adventures, directing Iron Man 2 and Cowboys & Aliens, and serving as executive producer on The Avengers.
He will reprise his role as Happy Hogan in Marvel Studios' forthcoming Iron Man 3, but will not direct this time round.