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Rex Features
Renner, who was confirmed to star in Ben Affleck's new movie The Town last week, also claimed that he had arranged a meeting with director George Miller.
"I'm fighting to do the new Mad Max film... That might be next summer," he said. "I'm screen-testing and meeting George Miller."
Renner's comments support rumours that Mel Gibson will not return to the action franchise.
Miller said earlier this year that he "probably would go a different route" in casting the film, which he said would be produced as a 3D anime.
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