The story quoted Greene as saying: "You feel bad for Mark, but at the same time, you want to win games. ... If you want to win games, you've got to try something."
Greene denied making the comments when talking to reporters Thursday.
"What I said is, 'We're 3-6, and things need to change,' " Greene said, according to comments distributed by the Jets. "I never said anything about changing the quarterback or anything about any single person on this team. I've been here four years, and I've never once said anything about anybody on this team."
Michael Silver, who wrote the story, wrote on Twitter that he stands by his column "100 pct" and accurately quoted Greene. Greene says he texted Sanchez when he heard about the story, and the two are fine.
The Associated Press contributed to this report.