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:
"They need to make one. And I wish them nothing but success in the future and if they want me to be involved in some way then I will, if they want to do a prequel or whatever, but as far as I know nothing is decided and it's not my business."
Director Paul Greengrass
And Actor Matt Damon showed some support:
"I'll just wait for him and when he wants to do one, we'll do it. I think it will happen down the road. We just don't have a script right now."
Actor Matt Damon
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!
:)