It's looking likely that the new Jason Bourne will be two-time Oscar nominee Jeremy Renner. The folks at Latino Review are reporting that director Tony Gilroy and studio Universal have agreed on The Town star to carry the franchise forward.
Renner was not apparently Gilroy's first choice; that was Oscar Issac - who's currently playing a deranged orderly in Sucker Punch - but Universal disagreed. An offer was then put out to Renner late last week, with no confirmation of an acceptance or turning down as of yet. Gilroy has said that The Bourne Legacy is not a reboot, sequel or prequel. It's a different character (all be it one with the same name) and will have its own unique feel.
Renner is particularly great casting if it moves forward with him in the role; but he's got Mission Impossible 4 due out at the end of year, so he may be cautious about secret agent overload. That said, it's an iconic part and there would be a huge challenge to make it his own.