Shockey is known for making outrageous and insensitive comments.
"I'll make him (Parcells) pay when we play them," Shockey is quoted as saying in New York Magazine. The issue hits newsstands on Monday.
After the Giants' 26-6 preseason loss at New England Thursday night, he denied making the homophobic comment.
"I really don't want to comment on something that's not true," Shockey told the New York Daily News. "I'm 100 percent sure I didn't say that. I think he (the writer) got it mixed up from something my friend may have called him."
The author, Chris Smith, told the Daily News that he has the interview on tape.
"He ended this monologue (on Parcells) by calling him 'the homo,'" Smith told the paper. "It's 100 percent accurate."
Shockey never played for Parcells, who coached the Giants to Super Bowl titles in 1986 and '90, but said in the interview he was upset at the coach for questioning his talent while working as a television commentator for ESPN last season.
2014: The Year in Music [PHOTOS]