Osweiler, 25, who started seven games last season and is scheduled to become a free agent on Wednesday, was offered a three-year, $45 million deal including incentives to become the starting quarterback of the Broncos with Peyton Manning retiring.
The offer falls between Nick Foles' $12.25 million per year deal and Andy Dalton's $16 million annual average.
But Osweiler is set to test the market unless the Broncos make a more competitive offer. Two lurking candidates to sign him to a deal closer to market value -- $19 million to $21 million per year -- are the Houston Texans and Cleveland Browns. The New York Jets would have to manuever to make room under the salary cap if they joined the bidding.
Ultimately, Osweiler is expected to stay with the Broncos but it is not known how high president and general manager John Elway is willing to go to retain him. Despite Osweiler's minimal sample size in the regular season, the Broncos drafted and developed him and no team has a better grasp for his ability, Elway said at the Super Bowl.