"It's not the intent to go that direction," Elway told 9News' Mike Klis.
The Broncos have no interest in trading for Romo, but were believed to be interested in him as a free agent. The news leaves the Houston Texans as the primary destination for the aging gunslinger, especially after the franchise traded Brock Osweiller earlier this month to the Cleveland Browns.
An injury history including two left collarbone breaks and a compound fracture in his back limited Romo's availability to just five games in the last two seasons. He was a Pro Bowl selection in 2014 after completing a league-best 69.9 percent of his passes for 3,705 yards, 34 touchdowns, and nine interceptions.
The Cowboys were expected to release the 13-year veteran earlier this month, but surprisingly held onto him. Romo, 36, is due $14 million in 2017 and $19.5 million in 2018. He has a $20.5 million salary in 2018.
NFL Network national insider Ian Rapoport reported Monday that the Romo saga "isn't ending anytime soon." He also said it could last past the 2017 NFL Draft, which is set for April 27.
According to multiple reports, Romo's other option, if he doesn't join the Texans, is retirement.