The team agreed to a one-year deal with the enigmatic punter on Tuesday, agent David Canter told The Associated Press.
The New England Patriots have one week to match the offer, which is incentive-laden and could be worth more than the $1.395 million he was due to make in Denver in 2006 before being jettisoned by the Broncos.
Sauerbrun lost his job in Denver when he was released after serving a four-game suspension at the start of the season for using the banned dietary supplement ephedra in a misguided attempt to lose weight and gain gusto for his workouts.
When no other team offered him as much as a look, he suggested he was being blackballed by the league. The Patriots signed him just before Christmas and he punted for them through the playoffs.
If New England declines to match Denver's offer, Sauerbrun would compete with last year's starter, Paul Ernster, whose superb performance during Sauerbrun's suspension contributed to Denver's decision to cut ties with Sauerbrun last October.
Sauerbrun has said he'd like to return to Denver but also feels a debt of gratitude to New England.
"Todd feels like Denver is a place where he has unfinished business," Canter said. "And he also feels a lot of admiration for the Patriots, who were the only team to give him an opportunity last year when a lot of other teams wouldn't."
Sauerbrun, a 13-year veteran who also kicks off, has a career punting average of 44 yards with a net average of 36. He made the Pro Bowl three straight times, between 2001 and 2003, when he was with the Carolina Panthers.
Sauerbrun said he knowingly took an over-the-counter weight loss product last summer that he strongly suspected contained ephedra, which the NFL banned after the death of Minnesota Vikings offensive tackle Korey Stringer during training camp in 2001. Players are randomly tested and can be suspended after the first violation.
That drew the ire of Broncos coach Mike Shanahan, who said the punter is the only player on the team who can be fat as far as he was concerned.
Sauerbrun, who packs 215 pounds on his beefy 5-foot-10 frame and who was fined by the Panthers for eating too much, said at the time that he worries about his weight all the time.
He also said he especially regretted letting down Shanahan, who gave him a fresh start after a trouble-filled stint in Carolina, and that he hoped he could make it up to him someday.
"Todd would love to play for Mike Shanahan again," Canter said. "He'd love to show Broncos fans that he is not a bad guy, and he wants to help the Broncos win a Super Bowl."