The Bourne Legacy star, who played the archer in The Avengers, admitted that he has no idea if he will be reprising the character in any of the upcoming Marvel films.
"It's a great character," Renner told MTV News. "There's a lot to explore there for me personally but I have no idea where they'll go with it."
He went on to say that ultimately he will not make the decision on Hawkeye's return.
"That's another sort of, [there are] puppeteers, they have their own ideas," Renner added. "I have no idea what's going on, people are probably more informed than I am of the reality of me being in another movie."
The 41-year-old recently insisted that he does not consider himself a replacement for Matt Damon in the upcoming Bourne film.
The Bourne Legacy is due for release on August 10 in the US and August 13 in the UK.
Watch Jeremy Renner in a clip from The Bourne Legacy below: