According to ESPN's Adam Schefter, Joseph will be let go after his one and only season as the team's head coach.
The Broncos entered Sunday's regular-season finale against the Kansas City Chiefs with a 5-10 record.
Schefter reported Sunday that the franchise has yet to make a final decision on Joseph's future.
The Broncos endured an eight-game losing streak from Oct. 15 to Dec. 3, with a number of losses being blowouts. The skid was the team's longest since 1967.
"Obviously, it's been a tough year for us," Joseph said. "And you learn as a coach that you can't ride the ups and downs of the season. You have to stay consistent because the message comes from the coach.
"So when things are not going right, I can't walk in and change my overall behavior when it comes to doing things right. I can't panic, and hopefully I didn't."
Joseph, the Broncos' first African-American head coach, replaced Gary Kubiak a year ago after the latter stepped down for health reasons.
Instability at quarterback, among other things, has plagued the Broncos this year. Trevor Siemian, Paxton Lynch and Brock Osweiler all started games in 2017, and Lynch was getting the call for the finale.
"He's just a truthful coach," Miller said in Joseph's defense. "It was just a tough hand that he was dealt. I feel that Coach V.J. is one of my favorite coaches that I have ever played with. I could relate to Coach (John) Fox and Kubiak and all of those guys. But Coach V.J. taking on the job that he had and still trying to finish the way that he is trying to finish, I respect him for that."
If the 45-year-old Joseph is let go, the Broncos would join a list of teams with head coaching vacancies or expected to have one. There could also be openings in Arizona, Chicago, Houston, Indianapolis and Cincinnati.
The Broncos, considered one of the NFL's most stable and successful franchises, would be looking for a fourth head coach in the past seven years.
"We still have good players. We have a great staff," Joseph said. "We have great support here from the operations side of things. It's been a winning program for a long time, so that part is not going to change. We have to make some tweaks, obviously, to get back to where we want to be. But I think we're really close."