The New York Daily News said several sources confirmed the relationship that reputedly began when Clemens, now 45, was a 28-year-old star for the Boston Red Sox and McCready, now 32, was 15 and singing in a karaoke bar.
"He (Clemens) flatly denies having had any kind of an inappropriate relationship with her," attorney Rusty Hardin told the Daily News. "He has considered her a close family friend. ... He has never had a sexual relationship with her."
Hardin added that Clemens' wife Debbie also knows McCready. The Clemenses married in 1984.
The Daily News said the revelation of the alleged affair could have an effect on Clemens' ongoing battle against steroid allegations. Clemens has sued former trainer Brian McNamee for defamation of character.
"The issue in Roger's suit against McNamee is Roger's reputation and how it has been damaged," Richard Emery, one of McNamee's attorneys told the Daily News. "If it's proved that he is a philanderer, his reputation is already damaged."
The Daily News article didn't include comments from McCready.