Nothing is ruling-out Renner showing-up in this other Bourne project. However, I'd expect it to be just Damon and Greengrass. Director Justin Lin has been linked for directing a couple of season two episodes of HBO's True Detective, it adds more fuel to the thought we'll see further production delays.
Jeremy mentioned to Collider he would be game to be apart of the third film, that's if his production schedule allowed him to. He's currently shooting Mission: Impossible 5, but with Bourne delays it's possible that Renner could be available for the April start on Captain America 3. The Russo Brothers are also open to the idea, and I'd love to see them work with the character. They've done wonders reworking both Rogers and Natasha. We've been hearing that Marvel has big plans for Hawkeye, as the Avenger will have a larger role in Age of Ultron. In the comics, Barton takes-on a leadership role as the team leader of The West Coast Avengers, a splinter group of the main lineup. There are already rumors that Steve Rogers starts putting together a second team by the end of Ultron.
“There are rumblings of Captain America 3. I don’t know what’s going to happen there. I’ve got to find the time, man (laughs). I’m trying to stay home and I can’t.”