GK Films' Graham King and Tim Headington will produce the film, which will utilize much of the same music that is heard in the Broadway production. Executive producers are Frankie Valli and Bob Gaudio.
The film, according to the industry paper, will likely be produced in partnership with Columbia Pictures.
No timetable or casting has been announced.
Logan won the Tony Award in 2010 for his play Red, about painter Mark Rothko. He received Academy Award nominations for "The Aviator" and "Gladiator." Logan also penned the screenplays for "Sweeney Todd," "Coriolanus" and "Hugo."
Jersey Boys, which is directed by two-time Tony Award winner Des McAnuff, was written by Academy Award winner Marshall Brickman and Rick Elice, with music by Bob Gaudio, lyrics by Bob Crewe and choreography by Sergio Trujillo.
The musical opened at the August Wilson Theatre on Broadway to critical acclaim on Nov. 6, 2005.
The musical is the winner of the 2006 Best Musical Tony Award, the 2006 Grammy Award for Best Musical Show Album, the 2009 Olivier Award for Best New Musical and the 2010 Helpmann Award for Best Musical (Australia).
Jersey Boys is the story of Frankie Valli and The Four Seasons: Frankie Valli, Bob Gaudio, Tommy DeVito and Nick Massi. According to press notes, "This is the story of how a group of blue-collar boys from the wrong side of the tracks became one of the biggest American pop music sensations of all time. They wrote their own songs, invented their own sounds and sold 175 million records worldwide - all before they were thirty."
The show is currently playing in New York; Las Vegas; London; Sydney, Australia; and in cities across the US on two national tours. A production will open in Auckland, New Zealand, in April.