There is a strong likelihood that Jeffery will sign with another team once free agency begins on March 9, the source said.
Teams have until Wednesday at 4 p.m. ET to use their franchise designation.
NFL Network first reported the news of the Bears' plans.
Jeffery's numbers took a hit the past two seasons because of injuries and a suspension, but the 2013 Pro Bowl selection is one of the most productive receivers in team history and is still an upper-echelon receiver, with 13 career 100-yard receiving games.
Despite playing under the $14.599 million franchise tag in 2016, Jeffery caught only 52 balls for 821 yards and 2 touchdowns in 12 appearances, as Chicago started three different quarterbacks -- Jay Cutler, Brian Hoyer and Matt Barkley. He missed four games after serving a suspension for violating the league's policy on performance-enhancing substances.
From 2013-14, Jeffery combined for 174 receptions, 2,554 yards and 17 touchdowns. He missed seven games due to a variety of injuries in 2015.
He was drafted by the Bears in the second round in 2012 out of South Carolina.