With no money up front, Collins preferred to stay retired rather than fill in until Caleb Hanie's sprained right shoulder healed.
"It was a no-brainer thing where they had an injury, and they called up a guy who was essentially retired," Collins' agent Brad Blank said on "The Waddle & Silvy Show" on ESPN 1000. "And they made an offer, and the player was apprehensive that he would just get used for a couple of weeks and then would just get released.
"All players have different stations in their careers and different stations in life. Todd Collins has played 15 years in the NFL, and it ended pretty well. He doesn't want to just go into camp for a few weeks and have that end his career. He'd rather just not make the effort at all and stay retired."
Quarterback Josh McCown, currently under contract with the Hartford Colonials of the UFL, also has been ruled out as a backup option, a league source said on Tuesday.
Hanie suffered a sprained throwing shoulder Saturday in San Diego. He will miss Saturday's game against the Oakland Raiders, so the Bears reached out to Collins, among others.
"What they said is, 'We'll give you a chance to come in and compete for that job. And if you're really good, you may be our backup. And if you're not good, we may cut you," Blank said. "Todd was apprehensive with no money up front and no guarantee ... he could have been released ... and it wouldn't have cost the Bears anything."
Blank said he left the door open with the Bears.
"If they want to assure him in the form of a signing bonus that he's not going to just come in and have his arm be used for a couple of weeks and then be released, I said 'Feel free to call back. My ears are open,'" Blank said. "What he rejected was the minimum salary with no signing bonus."
ESPNChicago.com reporter Jeff Dickerson contributed information to this report.