"There was so much developed in the three prior movies, as far as the tone and pace, the action, the authenticity… there were so many things I loved about the series," he said according to Flicks and Bits.
"Then to see what Tony Gilroy did with the new material and with this new character, it really opened up the world. For me, it was really exciting."
He continued: "At first I was hesitant, I wasn't quite sure how they would do it. But once I saw how clever it was I just jumped at the chance. It was a lot for me to play with. And what Matt Damon did, and what the previous directors have done, that was great.
"For those who love the franchise, I'm not replacing Matt, nor would I want to. It would never have been interesting if I was taking over and playing the same character. Matt is always the face of Jason Bourne and always should be."
Renner also revealed that he was impressed by the inclusion of real scientific advances in The Bourne Legacy.
"I liked this script because it was a very interesting way of continuing the story while honouring what came before. And with The Bourne Legacy, there's a science to it that is very real, and why would it not be?" he said.
"It's in this franchise where authenticity is its main foundation. There's no superhero-ness to him, to my character, it's just advanced science that is very plausible. And I think that's exciting."