History with quarterbacks coach Matt Cavanaugh and head coach Marc Trestman, coupled with the perception the club needs a backup behind Jay Cutler, makes recently waived former Jets signal caller Tim Tebow a logical possibility in Chicago, but the Bears aren't interested, according to an NFL source.

The Jets waived Tebow on Monday after a one-year stint in New York.

"Unfortunately, things did not work out the way we all hoped," Jets coach Rex Ryan said in a statement.

His next opportunity won't come in Chicago, according to the source, who indicated there is no interest on the part of the Bears.

Having served as a quarterbacks consultant before becoming the head coach at Montreal and later Chicago, Trestman worked with Tebow to help the signal caller prepare for the 2010 draft. As quarterbacks coach of the Jets in 2012, Cavanaugh tutored Tebow last season as the quarterback passed for 39 yards on 6-of-8 completions and rushed for 102 yards.

A former Heisman Trophy winner, Tebow landed in New York last March through a trade with the Denver Broncos.

The Bears opted to not draft a quarterback last weekend, and will go into training camp with Josh McCown as the primary backup to Cutler and second-year player Matt Blanchard serving as the No. 3 quarterback unless they add another signal caller before then. Bears general manager Phil Emery has said the team is comfortable with McCown as the No. 2 quarterback, calling the veteran a "glue guy," whose value goes beyond what he can do on the field.

"We are (feeling good about McCown)," Emery said. "The thing I've gained an appreciation for is his influence in this building in terms of helping other people get where they want to go. I'm more than comfortable that he can get on the field and help us win."