Gonzalez, who is widely regarded as one of the greatest players in NFL history, is yet to win a Super Bowl ring in his illustrious career, leading to speculation that he could leave the 2-5 Falcons before today's trade deadline.
The 37-year-old has already announced that the current season will be his last, and he revealed that he would be open to talks about a trade as long as the first move came from the Falcons.
"I totally understand it. Everybody out there needs to understand that I'm not naive to it. I see it, too. This is the last [nine] weeks of my career. And right now, things are looking, you never know. But, like I said, I love my guys on this team too much to go ask for a trade," Gonzalez told ESPN.
"It would be something that would come from them where they said, 'Hey, it makes sense because we could get something good for you and send you to a team that's a contender.' So I understand the thought process behind that. When [analyst] Jimmy Johnson says that it would be respectful of [the Falcons], I see that. And like I said, if that's something they wanted to do and they asked me, then, yeah, I would listen to them, of course. Yes, I would sit down with them.
"You've always got to listen to them in anything. I don't care if you're not open to it or [are], you still listen and see what's up. We'll know by [four] o'clock tomorrow. But, like I said, I'm not going to be the one to go asking for a trade. It will have to come from them."
Gonzalez has been linked with a return to the undefeated Kansas City Chiefs, where he spent 12 seasons between 1997 and 2008.