The move will come at the start of the NFL's free agency period and will allow the Cowboys' all-time leader in passing yards and touchdowns to sign with any team, including the Broncos.
The Broncos and Houston Texans, who signed former Denver quarterback Brock Osweiler last offseason, are expected to be the primary contenders for Romo, who is 78-49 in his career but never got the Cowboys past the divisional round of the playoffs.
Romo has not played a full 16-game season since 2012.
Romo had two back surgeries in 2013 and suffered two transverse process fractures in 2014. In 2015, he broke his left collarbone that forced him to miss seven games, then rebroke it in his second game back.
He underwent collarbone surgery in spring 2016, but in a preseason game, he suffered a compression fracture in his back, forcing him to miss most of the regular season.
While he sat out, Prescott helped lead the Cowboys to 11 consecutive wins and when Romo was healthy to return, Dallas stuck with the rookie. Romo played in the regular-season finale against the Philadelphia Eagles.
When Peyton Manning retired after the 2015 season after guiding the Broncos to the Super Bowl 50 title, general manager John Elway moved up in the draft to take Paxton Lynch out of Memphis.
During open competition in training camp, second-year quarterback Trevor Siemian, a seventh-round pick in 2015, won the starting job. He threw for 3,401 yards, 18 touchdowns and 10 interceptions in 14 games, going 8-6 after starting 7-2.
Lynch started two games as Siemian recovered from injuries, throwing for 497 yards, two touchdowns and one interception.
The Broncos went 9-7 last season after a 4-0 start and finished third in the AFC West, missing the playoffs for the first time since 2010.
If the Broncos acquire Romo, it's expected they will work to trade Siemian and keep Lynch.
And if Romo is with the Broncos in the fall, it sets up a rematch against his former team as the Cowboys will play at Sports Authority Field at Mile High next season.