Pelissero also reported that Buffalo could be interested in Minnesota quarterback Case Keenum.
Keenum is expected to become the first of the high-profile quarterbacks in the open market to agree to a deal.
The six-year veteran picked the flawless time for a career year before cashing in during free agency.
According to 9News Denver, Keenum's deal is expected to be a short-term agreement, suggesting it won't preclude the Broncos from taking a quarterback with the fifth overall pick in next month's draft if they so choose.
Now 30 years old, Keenum is coming off a career year with the Minnesota Vikings in which he completed 67.6 percent of his passes for 3,547 yards with 22 touchdown passes against seven interceptions.
The NFL Free Agency Frenzy is nearly like Christmas in March, and for Case Keenum his present is playing in Denver on Sunday's.
In 2016, when Trevor Siemian unexpectedly beat out veteran Mark Sanchez and first-round draft pick Paxton Lynch to win the Broncos' starting quarterback job, Elway almost acquired Keenum in a trade from the Los Angeles Rams but backed off.More news: Mystery $560M Powerball victor can remain a mystery, judge rules
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The Broncos haven't made the playoffs since their Super Bowl win to close out the 2015 season.
Six years ago, Elway landed Peyton Manning, the biggest free agent prize in National Football League history, following his release by the Colts and a series of neck fusion surgeries.
Just ask John Elway to say "rebuilding".
Elway said in recent weeks he still believed the team could get back into the postseason mix with an upgrade behind center.
The Broncos could still draft a quarterback. Elway has left open the possibility that Lynch could be the team's backup if he's ready to work on his game, but in the end, even one of Elway's most notable first-round picks couldn't avoid the team's current mission.
Or as Elway put it at the scouting combine: "I didn't say it".
Elway had said early in the offseason "for us to have a chance to get better we have to get better at that position". There were some things that we should have done, that we should have done differently that we didn't do.