Universal Pictures had originally hired Heights' Tony-nominated book writer, Quiara Alegria Hudes, to pen the screenplay, but Klein "has been brought in to give the priority project a fresh set of eyes," according to the industry paper.
Filming, under the direction of Kenny Ortega, is expected to begin in New York in August. The musical's creator and original star, Lin-Manuel Miranda, who earned a Tony Award for his score, will reprise his role as Usnavi for the motion picture.
The movie musical, Variety reports, will likely include most of the original Broadway score as well as one new song penned for the film.
Kevin McCollum, Jeffrey Seller and Jill Furman Willis, who produced the musical, are the film's executive producers.
In the Heights won four 2008 Tony Awards including Best Musical. Lin-Manuel Miranda won the 2008 Tony for Best Score (music and lyrics), Andy Blankenbuehler won the 2008 Tony for Best Choreography, and Alex Lacamoire and Bill Sherman won the 2008 Tony Award for Best Orchestrations. The musical is now in its third year at Broadway's Richard Rodgers Theatre.