Burress, who is out of football this season after catching eight touchdowns for the New York Jets last year, told ESPNChicago.com on Tuesday that he would be honored to join the Bears. Emery was asked about the report on Wednesday.
"We kind of look at (improving) every day," Emery said. "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. 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: 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, 35, caught 45 passes for 612 yards last season after spending the previous two years in prison for an incident in which he shot himself in the league in a New York City nightclub. He believes he still has plenty of football left, but he hasn't been given the opportunity yet this season.
"I don't think anybody saw this coming from my camp," Burress told ESPNChicago.com on Tuesday. "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."
Even the Jets, who have struggled mightily on offense this season, haven't called Burress.
"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."