The article on Tebowmania was written by Michael Silver and titled "The year of Magical Stinking: An Oral History of Tebow Time."
In it, Quinn was quoted as saying, "We've had a lot of, I guess, luck, to put it simply." He also said he felt the fans were the reason Tebow leapfrogged him on the depth chart when supplanting Kyle Orton as the starter after a 1-4 start.
"I felt like the fans had a lot to do with that," Quinn said in the article. "Just 'cause they were chanting his name. There was a big calling for him. No, I don't have any billboards. That would have been nice."
Quinn also said in the article that the way Tebow expresses his faith doesn't "seem very humble to me." Both men are Christians.
Quinn took to Twitter after the article's release Tuesday, saying the comments attributed to him did not reflect his opinion of Tebow.
Tebow "deserves a lot of credit for our success and I'm happy for him and what he accomplished. Most importantly, he is a great teammate," Quinn wrote.
Quinn said he's reached out to Tebow directly "to clear this up," adding, "I apologize to anyone who feels I was trying to take anything away from our team's or Tim's success this season."
Quinn also said on Twitter that "the resulting story was a completely inaccurate portrayal of my comments. I have addressed my disappointment with the writer and have reached out to Tim to clear this up."
Silver, on his own Twitter page, said "I quoted him accurately. Interview on tape."
In another entry, Silver said: "I have the transcript and take (sic) to back it up. I do agree that Brady is a standup guy, and his tone was not bitter."
Quinn is an unrestricted free agent whom the Broncos are considering bringing back to Denver.
He was Orton's primary backup when the season started but when Orton struggled, the Broncos' brain trust wanted to see what they had in Tebow, a 2010 first-round draft pick who made more than $7 million last season, including a big bonus that was paid before the season.
"They say we were giving him a hard time because he's a Christian. No, that's not it! We were giving him a hard time because he's terrible," Suggs said, according to GQ.
Tebow won seven of his first eight starts and produced a series of stirring fourth-quarter comebacks that made up for his poor passing and messy mechanics.
With Tebow at quarterback, the Broncos reached the playoffs for the first time since 2005, and they won their first game, against Pittsburgh, when Tebow connected with Demaryius Thomas on an electrifying 80-yard touchdown pass on the first play of overtime.
Thomas chimed into the latest Tebow rift on Tuesday, tweeting, "I'm tired of ppl talking about my QB.. If u ask me there's no such thing as luck.. It's hard work and determination.. That's all..."
After the Broncos lost at New England in the divisional round, football chief John Elway declared Tebow the starter heading into training camp this summer but stopped short of saying the third-year pro had won the job for opening day next season.
The Broncos haven't ruled out bringing back Quinn, who didn't take a single snap in his two seasons in Denver after being acquired from Cleveland in the trade for Peyton Hillis in 2010.
Besides Tebow, the only other quarterback under contract for next season is Adam Weber, who spent last season on the Broncos' practice squad.
The Broncos will try to add a couple of quarterbacks through free agency and the draft.
Elway, a two-time Super Bowl winner and Hall of Famer who rejoined the franchise last year, has said Tebow must morph into more of a pocket passer to succeed long-term in the NFL.
Coach John Fox reintroduced the option offense to the league last year and Tebow piled up yards on the ground, but he completed less than half his passes in both the regular season and the playoffs.
Tebow has already spent time working on his throwing motion and mechanics with UCLA offensive coordinator Noel Mazzone in Los Angeles this month. Mazzone also helped him work on his fundamentals coming out of Florida, where he was a three-time All-America, a two-time national champion and a Heisman Trophy winner.
Information from The Associated Press was used in this report.