Dumervil, the 2009 NFL sacks leader, has a restricted free-agent tender worth $3.168 million on the table. If he didn't sign by midnight, the team could have reduced the amount to 110 percent of his 2009 salary, which was $540,000.
Dumervil had 17 sacks in 2009 and became the first player in Broncos history to lead the NFL in that category. He was selected to his first Pro Bowl.
Despite his stellar season, he is in tough contract negotiations with the team.
On Friday, Dumervil said he didn't want to have his contract situation play out in public, and he doesn't feel the need to campaign for more money.
"I know my value. The stats speak for themselves so I'm not going to jump on the Elvis Dumervil bandwagon," he said. "I'm not that type of guy. I don't need to say much.
Dumervil attended this past weekend's minicamp even though he hadn't yet signed his tender.
Information from The Associated Press was used in this report.