But Bears wide receiver and returner Devin Hester thinks that would be "a waste of time."
Sources told CSNChicago.com that the Bears might have interest in McNabb after Caleb Hanie threw three interceptions Sunday. He has started two games, both losses, and has three interceptions in each game since Jay Cutler went down with a hand injury.
To make matters worse, the offense took another hit when Matt Forte suffered what looks to be a strained medial collateral ligament in his knee.
"Whatever we are doing is not working and we need to fix it fast before it gets too late," Hester told ESPN Radio's "Mike and Mike in the Morning."
Hester acknowledged that the Bears need Forte, but he thinks the Bears can turn it around. They were in the driver's seat for the NFC wild card but after the two losses are now 7-5.
Hester does not think that McNabb, who was cut by the Vikings last week and went unclaimed, will help the team get back on track, though.
"It's going to be tough right now to add a quarterback that hasn't played in a Mike Martz offense," he said. "It's one of the more difficult offenses to run, so to get a quarterback that hasn't been in that offense, right now it's going to be a waste of time. I guess we'll stick with the guys we have right now and hope we get better with those guys."
McNabb's agent, Fletcher Smith, said Saturday he was talking to "a couple of teams" during the weekend, but no team is prepared to make a move right now.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.