Woodson was cut by Green Bay in February.
While speaking with season ticket holders last week, Broncos vice president of football operations John Elway insinuated that the team could be looking to add an extra safety.
"Safety-wise, we feel pretty good," Elway said, according to the AP. "I think everyone is going to have their difference of opinions on what they think we need, but we did the best we could with what we thought were the most important needs for us. But we're always looking, and we're not totally done with anything.
"We're always looking to improve our team, and if there's a safety or somebody we see out there that can help us, then I think we do something there."
It seems like Woodson would be a solid fit, either at strong safety or to simply serve as an extra DB on passing downs.
Woodson, 36, admitted last month that he had drawn little interest, and that teams saw him as "ancient."
Still, it's hard to argue with Woodson's success. Though he's aging, he has always been a ball-hawk -- he's second among active players with 55 career interceptions -- and he was named 2009 NFL Defensive Player of the Year.