The espionage thriller sees Mission: Impossible - Ghost Protocol star Renner play Aaron Cross, an agent from a covert government programme similar to the Treadstone facility that trained Jason Bourne (Matt Damon).
Renner and writer/director Tony Gilroy have replaced Matt Damon and Paul Greengrass on the Bourne franchise, although there is scope for Damon to return in the future.
"This one still has to be successful, but maybe eventually Matt Damon and I could do one together," Renner said. "That would be kick-ass. I love Matt."
Edward Norton, Oscar Isaac, Rachel Weisz, Joan Allen and Albert Finney will co-star in The Bourne Legacy, which opens in cinemas in August 2012.
> Jeremy Renner reveals 'Bourne Legacy' character name, plot details
> Digital Spy's Top 20 Must-Watch Movies for 2012
Watch Matt Damon and Paddy Considine in the Waterloo station sequence from The Bourne Ultimatum below: