Warner Bros. and director Peter Jackson are seeking to turn the planned two-film “Hobbit” franchise into a trilogy, a move that could pay off in bigger box office returns, according to people familiar with the situation.

The Burbank film studio originally planned to release two “Hobbit” movies based on J.R.R. Tolkien’s literary prelude to “The Lord of the Rings” trilogy, and principal photography on those two pictures finished in New Zealand this month. The first is set to come out in December, followed by the second in December 2013. The two films combined cost about $500 million.

But Jackson has concluded that there is enough material from the book, as well as the extensive appendixes to “The Lord of the Rings,” to make a third film, according to three people who were not authorized to speak publicly. New Line Cinema, the Warner Bros. unit overseeing production of the movies, is eager to see it happen, and talks are underway with actors and others who would need to sign off on the plan.

A third film is far from a certainty, however, because there are numerous rights-holders and actors with whom new deals must be made.