According to Rapoport, Miller will speak publicly Friday and is "at home resting and in good spirits."
The Broncos issued a statement on Miller's diagnosis:
"After experiencing flu-like symptoms, Denver Broncos linebacker Von Miller has tested positive for COVID-19. Von has elected to share his diagnosis publicly to emphasize that anyone can be afflicted with coronavirus.
"Von is doing well and recovering at home in self-isolation. He remains under the care of team doctors, who are following all coronavirus treatment procedures to ensure a safe environment for Von and our community.
"Von is the first member of the Broncos' organization known to have tested positive for COVID-19."
Rapoport noted the Broncos know about Miller's positive test.
Miller opened up to CBS Denver on April 11 about what he was doing with the coronavirus pandemic shutting down the sports world as a whole:
"I was in San Francisco before, working on the sand and the stairs. When the coronavirus started going crazy, we came back. I've got a gym here at the house. It's still not the same as San Francisco, but we're going to be able to hold it off until we can get back to San Francisco.
"Everybody's going through the same thing. It's a tough time. It's a crazy time."
While Allen was the first player to test positive, New Orleans Saints head coach Sean Payton also tested positive and has since recovered from COVID-19. What's more, ESPN's Adam Schefter reported one member of the Los Angeles Chargers organization tested positive for the coronavirus with two others showing symptoms.
Michael David Smith of Pro Football Talk noted former players Orlando McDaniel and Tom Dempsey died from the disease.
The NFL has made a number of adjustments to its offseason during the pandemic. In-person interviews and meetings with free agents and draft prospects were largely impossible to conduct, all public events surrounding the draft in Las Vegas were canceled and the league and its players association agreed to a virtual voluntary offseason program.
Miller has been with the Broncos his entire career since they selected him with the No. 2 overall pick of the 2011 NFL draft. He is an eight-time Pro Bowler and three-time All-Pro selection who won the Super Bowl MVP to cap off the 2015 campaign.