A Marvel Studios spokesman declined to comment.
The 42-year-old Ruffalo -- not known for starring in action movies -- is currently starring in the The Kids Are All Right with Annette Bening and Julianne Moore. He also has appeared in the movies Shutter Island, Zodiac and Collateral.
Earlier this week, Marvel announced the studio would not be asking Ed Norton to reprise his role from the 2008 film The Incredible Hulk. Norton replaced leading man Eric Bana who starred in the 2003 film Hulk. (The TV series The Incredible Hulk ran on CBS from 1978 to 1982, featuring Bill Bixby as Bruce Banner and Lou Ferrigno as the Hulk.)
Both movies had strong opening weekends at the box office but fell off considerably in subsequent weeks. The first, directed by Ang Lee, received mixed reviews, while the second, helmed by Louis Leterrier, was more warmly received.
News of the offer to Ruffalo was first reported by Deadline Hollywood.
What do you think? Would Ruffalo be a good Banner?