But Bears GM Phil Emery said Wednesday that he's happy with the receivers currently on the roster.
"Every day we look at the availability of the veteran players that are out there and whether they can add to our mix in a positive way," Emery said. "So that we can win championships and continue to work towards winning championships. So if there is a player out there we feel is going to make our mix better, would we approach them? Yes. But it just depends on the player, depends on the situation, depends on what our needs are.
"I would say to answer more specifically to that question (about whether he'd be interested in Burress): We feel very good about our wide receiver depth. We added a player to our practice squad (Kamar Aiken) to make sure we were in a good competitive situation for practice. We continue to improve. That's where we are with that group."
Burress remains out of football despite catching 45 passes for 612 yards and eight touchdowns for the New York Jets last season. Considering that came after two years away from the game as he served time for an incident in which he accidentally shot himself in the leg in a New York City nightclub, some wonder why no team is taking a chance on the 6-foot-5 Burress improving on those numbers this season.
Is it the fact he's 35, or are there character issues?
"I don't think anybody saw this coming from my camp," Burress said. "I just wanted to get my legs under me (last season) and get back to being the explosive football player like before. People look at me being 35 and say I can't do some of the things I was able to do, but I did that last year after being off 30 months.
"It's a mystery to me and everybody else. But I remain optimistic."
Some thought the Jets might call Burress after a season-ending injury to Santonio Holmes and their struggles on offense. Coach Rex Ryan, who recently praised Burress' character, lamented some dropped passes after Monday's loss to the Houston Texans. But the Jets have not called.
"They want to go younger," Burress said. "That's what it looks like this league is becoming; all the veterans are sitting on the sidelines watching from home.