There have been talk about a possible Bourne 4 movie since quite a long. Back in 2009 it even announced that the next Bourne movie would actually be a prequel and the production should have start in 2010. But over neither Paul Greengrass nor Matt Damon have been much enthusiast about keeping the franchise alive... They even stated that the franchise could do fine without them (because they couldn't agree on a script with Universal according to the rumor), dashing hope of a Bourne 4 movie as a result.
But Director Paul Greengrass recently re-opened the door to a new Bourne movie:
And Actor Matt Damon showed some support:
So since Matt Damon is getting older, and because Universal doesn't want to waste the franchise, I think they will come up with a consensual solution. And I'm pretty sure that we'll get to watch the movie Bourne 4, prequel or sequel, sooner or later!