Henry Cavill and director Zack Snyder's comic book blockbuster is not due in cinemas until 2013, but the studio has reportedly drawn up a shortlist of three names to write a follow-up.
Harry Potter's Steve Kloves, Clash of the Titans writer Travis Beacham and Raiders of the Lost Ark's Lawrence Kasdan are all said to be in the running to pen Man of Steel 2, according to website ThinkMcFlyThink.
Superman star Cavill recently admitted that he jumped up and down with joy when he found out he had won the role earlier this year.
"My smile was absolutely enormous," he said. "I was trying very, very hard to play it cool on the phone with Zack Snyder when he called me."
Man of Steel, co-starring Amy Adams, Russell Crowe, Michael Shannon, Kevin Costner and Diane Lane, will open in cinemas on June 14, 2013.
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