Burress, who hasn't played since August 2008, served nearly two years for carrying an unlicensed gun after accidentally shooting himself in the thigh in a New York nightclub.
"Oh without question, without a doubt (the Bears are among his top three choices)," Burress said on "The Carmen, Jurko & Harry Show" on ESPN 1000. "My decision making is going to come down to what I said, playing with an elite quarterback, playing with a running game, playing with a great tight end, and Greg Olsen is already that guy, in my estimation he'll be a Pro Bowler this season.
"That's the same situation I went into when I made my decision to go to New York (to play with the Giants), and it's a pretty similar situation."
"As a receiver, I have a lot of respect for Jay Cutler," he said. "I feel he's a phenomenal talent. With the right tools put in place ... I think he can go all the way to the top."
There's no indication if the Bears would be interested in Burress, although linebacker Brian Urlacher recently said Burress would be welcomed in the Bears' locker room.
"I'm a big fan of his," Urlacher said on ESPN 1000's "The Waddle & Silvy Show" on June 23. "Always been a big fan of his, football-wise. Every time he plays against us, he gives us fits. He's a tough matchup for any corner. He's a big guy (6-foot-5, 232 pounds), good red-zone guy. I don't know how fast he is, but that doesn't really matter when you're that good."
Bears fans also expressed their admiration of Burress via Twitter, and it apparently made an impact.
"It's just been love," Burress said. "And that's what I love about the whole situation. Any city that you go to, you want to be embraced by the fans and by the city. And that really plays a lot into the decision making, going into a great organization.
"As a player you just want to be embraced. That's what I love about Chicago fans, they're passionate about football, they're passionate about their sports, their passionate about their basketball. It's one of the best cities in the world."
"I can't say where I'm already going," Burress said. "There are a lot of situations for me to go into. It's not solely going to be based on how much I'm going to be making. It's going to be based on me putting myself in a great situation. Me going to a city where I'm going to be embraced by the fans, and going to an organization that I can help and make the other players around me have the impact, go out and score some touchdowns and hopefully win the Super Bowl."