Dumervil signed a six-year, $61.5 million contract in 2010 when Josh McDaniels was coaching the team and before John Elway joined the Denver front office. The seven-year veteran is scheduled to make $12 million in 2013.
The team wants Dumervil to take a cut or restructure his contract, according to a person familiar with the situation, who spoke to the Associated Press on condition of anonymity because details of the negotiations were not public.
The Denver Post first reported about the team's request.
Dumervil had 11 sacks last season, second on the team behind Von Miller. Dumervil led the league with 17 sacks in 2009.
The Broncos need more cap space while trying to shore up their interior defensive line, cornerback and running back positions. Peyton Manning will earn $20 million in 2013 and if the Broncos had Dumervil play at his current number, those two would account for more than a quarter of their cap space.
Among the pass rushers on the market this season include Manning's former teammate with the Colts, Dwight Freeney.
Dumervil's agent, Marty Magid, did not respond to an email message from the AP. He told the Post he did not classify the request as a pay cut.
"I'm going ahead with this being a restructure," Magid said. "If we can meet on some common ground, there's a potential we can get it done. If we can't, they'll have to make a decision."