My guess no, the three Bournes have been good and when a sequel comes out there is always talks of another one that might come out in the future and I do not think they would want to risk it and end it on a bad note. But according to StarPulse Damon said if the director of the movies calls him up in several years he would be in it ASAP.
I would love to see another Bourne since those movies are just great movies; they have great action along with some comedic relief. It is not direct comedy, and even the actors do not laugh, what I am talking about is what Bourne goes into the chiefs office and call him from his office phone and Jason asks where he’s at and the chief says, I’m in my office. Bourne then returns saying, well if you were we would be having this conversation face to face. 
That right there to me is just hilarious and I would think so to others. Then there is the action, and I do not think I have to get into that at all with these movies since it is everywhere in them.
Source: StarPulse