Cruise, 48, starred in three previous "Mission" movies before making "Protocol," which is due in theaters next year.
Renner, 39, was nominated for an Oscar for his work in 2009's "The Hurt Locker." He will soon be seen in the superhero flick "The Avengers."
"It's a franchise to potentially take over," Renner told MTV News about his possible succession in the "Mission" series. "I can't predict the future and what they want, but that's certainly the idea."
The actor went on to say he couldn't reveal whether the changing of the guard is written into the plot for "Protocol" or if it might happen in another movie.
"I can't really go into the details of the script, because that's still evolving," he said. "It's Tom's baby. He's the engine behind the thing. What happens after that, we'll see."