LOS ANGELES (Reuters) - He said he would be back, and now Arnold Schwarzenegger is doing just that.

The action movie hero turned politician is attached to star in a new "Terminator" movie being shopped to Hollywood studios, an industry source said on Wednesday.

Schwarzenegger, 63, who played the killing machine cyborg in three of the blockbuster movies with the catch phrase "I'll be back", is on board to reprise a role that helped make him one of Hollywood's most successful and recognizable stars, the source said.

The news follows the end in January of Schwarzenegger's two terms as governor of California, and his announcement in February that he was ready to take movie offers again. He has already announced he is developing a TV show and comic book based on his political nickname "The Governator."

Industry website Deadline Hollywood reported that Schwarzenegger's talent agency Creative Arts Agency (CAA) was presenting a proposal regarding the "Terminator" this week to major Hollywood studios that would revive one of the industry's most successful franchises.

CAA declined to comment on the report.

Deadline Hollywood said there was no screenwriter attached so far. It was unclear whether director James Cameron, who wrote and directed the first "Terminator" movie in 1984, would be involved in the proposed new film.

Schwarzenegger starred in three "Terminator" movies but actor Sam Worthington took the main cyborg role in the fourth installment, "Terminator Salvation" in 2009.

The four movies have grossed more than $1.4 billion at worldwide box offices.

Schwarzenegger put most of his movie star life on hold while serving as California's Republican governor from 2003-2010. But he made a well-received cameo appearance in the 2010 movie "The Expendables" along with other aging action heroes Sylvester Stallone and Jet Li.

(Reporting by Jill Serjeant; Editing by Peter Henderson)