The move was confirmed by a person familiar with the decision who spoke on condition of anonymity because the announcement hadn't been made.
The Broncos declined comment, but were expected to announce a transaction later in the afternoon. Sauerbrun is the only punter on the Broncos' roster.
Sauerbrun faces legal trouble stemming from an incident outside a restaurant in early December. He's scheduled to appear in court Jan. 15 on an assault charge.
The story was first reported on the Web sites of The Denver Post and the Rocky Mountain News.
It is the second time Sauerbrun has been cut by the Broncos.
He was suspended for the first month of last season after using a banned dietary supplement. Upon his reinstatement, the Broncos and Sauerbrun went separate ways and he signed with New England.
The 38-year-old Sauerbrun returned to Denver on a one-year, $1.4 million contract after being granted his release from the Patriots last spring.
Sauerbrun was averaging 46.8 yards a punt, with a net average of 36.1.
However, the Broncos have struggled on special teams. Denver gave up a 75-yard punt return to Chicago's Devin Hester and then Sauerbrun had another kick blocked in Denver's 37-34 loss to the Bears in overtime.
Sauerbrun lost his starting spot to Paul Ernster last season while serving his suspension. He had used ephedra in an attempt to lose weight and gain extra energy for his workouts.
(Copyright Associated Press, All Right Reserved)