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Mario and Luigi are heading to the big screen in one of the highest-profile licensing deals by a Hollywood studio in years.

Illumination Entertainment, which makes animated films for Universal Pictures, is close to an agreement with Nintendo to make an animated “Super Mario Bros.” movie based on the 32-year-old videogame series about a pair of sibling plumbers who fight evil turtles and mushrooms in a fantasy kingdom, said people with knowledge of the discussions.

Nintendo’s marquee characters have long been tempting to Hollywood, particularly now that the movie business is driven by globally popular franchise films featuring well known brands like Marvel superheroes, “Fast and Furious” and Harry Potter. The dozens of Super Mario Brothers games and their spin-offs are widely believed to be the best-selling videogame franchise ever, having sold more than 330 million units total, according to Nintendo.

Other Hollywood studios have sought the Super Mario Brothers rights in the past, according to people familiar with the discussions.

Illumination, which made “Despicable Me,” “Minions” and “The Secret Life of Pets,” has been talking to Nintendo for more than a year about the movie, according to the people who know about the recent talks. The potential deal follows an agreement Universal’s theme-parks unit made with Nintendo two years ago to build attractions based on Marioand other characters.

A Nintendo spokesman declined to comment, as did an Illumination spokeswoman.

Universal finances and releases films produced by Illumination, which it co-owns with the animation company’s chief executive, Chris Meledandri.

Nintendo hasn’t made deals for movies or TV shows based on any of its marquee characters since 1993’s commercially and critically disastrous “Super Mario Brothers” starring Bob Hoskins, John Leguizamo and Dennis Hopper. Since then, its only cinematic efforts have been 20 inexpensive children’s animated movies based on its “Pokémon” games that were produced by an affiliate.

The most complicated issue in the negotiations between Illumination and Nintendo has been making the Japanese videogame company feel confident it will be involved enough in the creative process, said one person close to the talks. Nintendo’s creative guru, Shigeru Miyamoto, who created Mario Bros., has been part of the talks and likely will be a producer on the movie, along with Mr. Meledandri, this person said.

The agreement could allow Illumination to make multiple “Super Mario” movies, though only one is currently planned, this person added. It would be animated by Illumination’s Paris studio Mac Guff and is in the early stages of development, meaning it likely wouldn’t come out for several years.

Nintendo CEO Tatsumi Kimishima said in an interview last year with Japanese newspaper Asahi Shimbun that the company was in talks with several Hollywood studios about making movies based on its games. In an April analyst briefing, Mr. Kimishima said the company is making theme-park and movie deals less for the potential profits from licensing than for the additional sales revenue that could come from “synergy with the dedicated videogame business.”

Videogame movies have had a relatively poor record at the box office. Last year’s “Warcraft” was a flop in the U.S., though it did well in China, and other disappointments have included adaptations of “Doom,” “Need for Speed,” “Prince of “Persia” and “Assassin’s Creed.”

Nonetheless, they remain attractive to Hollywood. Time Warner Inc.’s Warner Bros. and Metro-Goldwyn-Mayer Inc. in March will release a reboot of “Tomb Raider,” after a pair of films in the early 2000s based on the games about an explorer and action hero had mixed results. An “Angry Birds” animated movie last year performed decently and a sequel is scheduled for 2019.