The Chicago Tribune first reported the Bears contacted Maynard on Monday to inform him of their plans.
According to the source, the punter was told by the coaching staff in late January that his chances of returning to the team were slim during an exit physical following the NFC Championship Game loss to the Green Bay Packers.
The team took issue with Maynard's statistical performance in 2010, when the veteran had an average of 40.1 yards per kick to go along with a net average of 35.2 yards. Some in the organization believed Maynard, 37, is no longer suited to kick in a cold-weather city like Chicago.
However, Maynard is still considered one of the top directional punters in the NFL, and placed 24 punts inside the 20-yard line last year. It's believed the veteran, one of the most decorated punters in league history, wants to continue his career and suit up for a 15th NFL season.
Jeff Dickerson covers the Bears for ESPNChicago.com and ESPN 1000.