ESPN's Jeff Legwold reported Ware was given $2 million to sign, and both sides see him as a third-down pass-rusher.
On Feb. 27, Mike Klis of KUSA reported the Broncos began speaking with agent Pat Dye Jr. about the situation.
Ware was scheduled to count slightly more than $11.6 million against the cap in 2016, which was the final season of his deal, per Spotrac.
The 33-year-old edge-rusher showed he can still perform at a high level, though. He racked up 7.5 sacks in 11 regular-season games and added 3.5 more during the Broncos' run to the Super Bowl 50 title.
Nicki Jhabvala of the Denver Post passed along comments from the veteran after the season, and he confirmed his intention to keep playing.
"I don't think about retiring," Ware said. "God still wants me to play. That's why I'm doing what I'm doing. When I start bringing the cane out, you guys make sure that you tell me, 'DeMarcus, it's time to hang the cleats up.'"
The KUSA report noted the Broncos also have lingering concerns about a bulging disc in the lineman's back, which adds another wrinkle to the equation.