Gilroy penned the first three films in the action series, which featured Matt Damon as Jason Bourne, and he was handed the job of director after coming up with a new plot for the forthcoming The Bourne Legacy.
The Michael Clayton filmmaker admits he struggled to find a leading man after first approaching Renner - only to be told he was too busy to take on the project - and he was left scrambling to fill the role until the last minute.
He tells U.S. breakfast show Good Morning America, "This movie, I think, came out of desperation. Matt had gone, Jason Bourne was no longer in the picture. I talked to a lot of people, tried to figure out where to go next (with the story)...
"Jeremy was not available for months and months. His name finally popped up (as available) as we were getting desperate and (producer) Frank Marshall and I ran over to Berlin and sat down and had dinner with him and he was exactly what we were looking for."
Gilroy admits he had a much easier casting experience with Renner's new co-star Rachel Weisz.
He says, "Rachel, I cast right away. I didn't search for Rachel. (We met) on Monday and by Wednesday she was cast!"