"I haven't coached Kirk Cousins, so I can't speak to that to be honest," Joseph said. "He's a Washington Redskin at the moment, so I can't speak to that.
"But obviously watching the guy over the years, he's a good football player. He's thrown for over 4,000 yards the last three years, and that's tough to do in this league. He's a good one, but I'll leave it at that."
While Joseph publicly didn't tip his hand, the Broncos' quarterback carousel did them few favors last season. Denver has Trevor Siemian, Paxton Lynch and Chad Kelly on its roster, with Joseph saying all three are in the mix for next season.
"As of now, yes. We've got two guys on the roster, well three actually with Chad Kelly," Joseph said. "We've got Trevor, we've got Paxton and we've got Chad Kelly. Absolutely they are. I can't speak to the future right now. Right now, they are our quarterbacks."
The Broncos, who finished with a 5-11 mark this past season, have had trouble getting consistent production out of the quarterback position since Peyton Manning retired after winning the Super Bowl.
In 2017, Siemian, Brock Osweiler and Lynch combined to complete just 58.7 percent of their passes for 3,668 yards with 19 touchdowns and 22 interceptions for a 73.0 passer rating. Kelly, who was a seventh-round pick in 2017 and a nephew of Hall of Famer Jim Kelly, is healthy after missing his rookie season with a wrist injury.
The Broncos could also look toward the quarterback position with the fifth overall pick in the 2018 NFL Draft.
Cousins is expected to fetch a high price on the free agent market this year. He is coming off a season in which he completed 64.3 percent of his passes for more than 4,000 yards with 27 touchdowns and 13 interceptions for a 93.9 passer rating with the Redskins.