Gonzalez said he will not ask for a trade, so if the 37-year-old is going to be traded, he said, "It will have to come from them."
The Falcons are 2-5 after losing to the Arizona Cardinals on Sunday and are slowly seeing their playoff chances slip away.
The NFL trade deadline is 4 p.m. Eastern on Tuesday.
"I totally understand it," Gonzalez said to ESPN.com. "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. 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."