It seems a possibility, according to actor Jeremy Renner (28 Weeks Later):

But Empire’s conversation with Renner took place after Iron Man 2 wrapped so, unless they go back and add him in reshoots, all sneaky like, it seems more likely that he’ll crop up in Thor or The First Avenger: Captain America. Does Renner have inside info? “If I was a betting man, I would bet that Hawkeye would probably show up in Thor, and then be in The Avengers,” he said. “But do I know for sure? I can’t say. But I’d love for that to happen. It’d be fun.”

From this article from EMPIRE.

Renner hints that he could be up for the role of Hawkeye, both in the Thor cameo and in Captain America, but also dismisses that he’s up for the role of Cap himself:

“I don’t know if I’d be right for Captain America,” said the 38 year old actor, who’d previously been linked with the role of Cap on that there internet. “I met with the Marvel guys, actually, but we didn’t talk about Captain America. But one of the writers, Zak Penn, we’ve become friends over time and he was thinking maybe Hawkeye could be interesting. He sounds like an interesting character.”

I liked Renner in 28 Weeks Later, and I’m pretty sure I haven’t seen him in anything else, but, according to IMDB, he was also in The Hurt Locker, and is on the TV show, The Unusuals.  I could definitely see him taking on the role of Hawkeye.

What say you?