"I think I've made it very clear to them [Denver management] that I want to be a Bronco," Knighton told ESPN's Josina Anderson on Wednesday.
Knighton, a team captain this past season for the Broncos, was a key voice in the locker room and a key part of the team's defense, especially on early downs.
He said he would be willing to take "somewhat of a hometown discount" but that he also wants to feel he is receiving fair market value for his position. He said the interest in him remaining put doesn't appear to be mutual at this point.
"To be quite honest with you, it's frustrating and it's somewhat disrespectful just knowing how important I was to the team and what the defense could've been without somebody like me," he said. "It's almost like, the longer they wait, the worse it is going to be."
One team that might be in the market for Knighton if he doesn't re-sign with Denver is in the Bay Area.
Oakland Raiders coach Jack Del Rio, who can't specifically talk about Knighton until the free-agent negotiating window opens in early March, made it clear Wednesday that he likes the Broncos defensive tackle plenty.
"We drafted him. We thought at that time he was kind of a dancing bear type," Del Rio said at the NFL's scouting combine. "A big, powerful man that could stay on his feet and run down the line. So, you know, this game is about big, powerful men so that the guys that have the skill level can do their things. So this big, powerful man played well in Jacksonville. We got back together; he played well in Denver, and so I appreciate that. I respect that. We have to have those kinds of people in our trenches on the offensive and defensive line in order to play the football we expect to play."
Knighton told Anderson the Raiders would be a natural destination for him if the Broncos don't re-sign him because of the history at work between him and Del Rio. Oakland's new coach was the Jacksonville Jaguars' coach when the team selected Knighton in the third round of the 2009 draft, and he was the Broncos' defensive coordinator when Knighton signed in free agency in 2013.
"There's been a lot of talk about me going to Oakland because of coach [Jack] Del Rio," Knighton said. "He and I have a great relationship. I know his defense. I know exactly how he wants his nose tackles to play and I am a very loyal person. He stuck with me ... and he is a big part of me being in Denver. So if things don't work out, he is definitely the first person I would like to talk to."
For his part, Broncos coach Gary Kubiak said Wednesday that the team hopes to retain as many of its free agents in the coming weeks as possible, including Knighton.
Knighton would be a nose tackle in the Broncos' new 3-4 defense.
"We've got a few [free agents] obviously," Kubiak said. "The key in this business is holding your football team together and getting better at the same time. We've got some key free agents. ... I know we're going to do everything we can to hang on to our players, but at the same time you have to put yourself in position through free agency and the offseason to get better as a football team. John [Elway]'s track record has proven he's doing a great job of that, so I'll leave that to him. We would like to hang on to everybody. We want to keep the team intact as best we can."
ESPN.com's Jeff Legwold contributed to this report.