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."

Cutler expressed similar sentiments, and suggested the team's decision to keep McCown as the No. 2 came after it explored other options.

"You have to trust the scouts and the coaching staff," Cutler explained recently during a voluntary veteran minicamp. "I think we had a lot of options for (backup) quarterback, and sifted through and ended up with Josh. He brings a lot of value in the room, football knowledge. He's been able to push us mentally more than anything."

Trestman also seemed comfortable with the idea of McCown playing the No. 2 role, saying he's "pretty lucky walking into a room with two guys (in Cutler and McCown) with that much football behind them that they can transition into other language and other ways of doing things."

As for Tebow, Cavanaugh expressed support for his former pupil. The new Bears quarterbacks coach also suggested that a team that takes on Tebow needs to give the quarterback a definitive role, which wasn't done in New York.

With the Jets, Tebow played somewhat of a gimmick role in plays designed to take advantage of his ability to run. Tebow never received a real opportunity in New York to play as a conventional quarterback.

"I think one of the things that you've got to be sure about when you do it is that -- why doesn't New England do it? Why doesn't Denver do it? Why doesn't New Orleans do it? They don't want to take those (quarterbacks) off the field," Cavanaugh said shortly after he was hired when asked about Tebow. "We were probably less (convinced) about how much we wanted to get (Jets starter Mark) Sanchez off the field to do that. So it was something we toyed with.

But to be fair to Tim, we didn't use it enough to let him be productive in it. So you better be sure when you decide to do it."

Given Cutler's skill set as a mobile passer, Tebow's ability wouldn't be needed in Chicago's offense, which in 2013 will incorporate some read-option plays.

"Wherever (Tebow) is at next, I think he's a good football player," Cavanaugh said. "I hope he gets a chance to play more."

The Bears aren't the only team to be linked to Tebow. As a native of Jacksonville, Fla. and former star of the Florida Gators, Tebow has long been linked to the Jaguars. In fact, the team took considerable criticism when it decided in 2010 against drafting Tebow.

When new general manager David Caldwell took over for Gene Smith back in January, he quickly put to end any speculation of possible homecoming for Tebow, saying "I can't imagine a scenario in which he'll be a Jacksonville Jaguar -- even if he's released."