Winter's Bone star Hawkes was first linked to the part of the comic book villain earlier this year, though British actor David Morrissey eventually won the role.
"They offered me the role, and I just felt there would be someone else who could do it better," Hawkes told MovieWeb.
"I was flattered, and I took a look at the series. It held interest for me, but I just didn't feel like I was the guy for it."
He added: "Yeah, it was nice of them to ask, and it's a good show... They came to me and sent me the graphic novel and the first two seasons. I took a look at them, and just didn't feel like it was for me."
Hawkes revealed that his final decision was influenced by the fact that The Walking Dead featured commercials when first broadcast.
"I have to be careful of what TV shows I choose, particularly ones that have commercials in them, because it's going to be a different kind of television show," he said.
"There are going to be sponsors. No matter how good the show is, if there are commercials, it's going to be a different show, to me. That's just my personal feeling."
The Walking Dead creator Robert Kirkman has insisted that State of Play star Morrissey will be "awesome" as The Governor.
"I think he's really going to knock it out of the park," said the writer. "He has tremendous scale and scope to his acting abilities. I think people are going to be shocked and amazed by the things we do with The Governor in season three."
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Watch John Hawkes in the trailer for Winter's Bone below: