A 10-year veteran, the 31-year-old Jennings has seen his role diminished in recent weeks.
"Chicago has treated me well, greeted me with open arms and gave me an opportunity," Jennings told ESPN's Josina Anderson Sunday. "I was able to make the best of it. But now, with the changes from the general manager to the coaching staff, I think it's time for a change for me. I'm excited about what is next."
Five Bears' cornerbacks played in the club's 21-10 preseason loss to the Cincinnati Bengals on Saturday before Jennings entered the game late in the second quarter.
Bears head coach John Fox was asked after Saturday's game if Jennings had been reduced to simply fighting to stay on the roster.
"I think everybody is. There's 90 people -- do the math," Fox said.
Jennings underwent knee surgery in the offseason, which limited his involvement in the Bears' voluntary workout program.
A 10-year NFL veteran, Jennings signed a four-year, $22.4 million extension on Jan. 2, 2014.
He led the NFL in interceptions in 2012 with nine, tied for second-most in one season in Bears history.
Jennings' $4.4 million 2015 base salary is guaranteed.
Jennings entered a guilty plea in late July for reckless driving and speeding that allowed for the dismissal of a DUI charge stemming from his arrest in Gwinnett County, Georgia, on Jan. 7.
He will not face jail time, but the sentence for the reckless driving charge is 12 months of probation, a fine of $800 and court costs. Jennings' punishment also includes 40 hours of community service and mandatory attendance in risk-reduction classes.