Parrella declined to name Radomski's clients.
The story was first reported by the New York Daily News.
Radomski, who worked for the Mets from 1985-95, has agreed to cooperate with the MLB investigation being led by former Senate Majority Leader George Mitchell.
"We look forward to working together with federal law enforcement toward our shared goal," Mitchell said in a statement.
Radomski dealt human growth hormone, deca-durabolin and testosterone, among other drugs, according to a search warrant affidavit obtained by the San Jose Mercury News. The warrant had some information blacked out, including what appeared to be players' names.
According to the warrant, Radomski became a major source of drugs for baseball players after federal investigators shut down Bay Area Laboratory Co-Operative in Burlingame. The case is being handled by the same federal investigators who netted guilty pleas from BALCO founder Victor Conte and Barry Bonds' personal trainer, Greg Anderson, among others.
Howard Johnson, a Mets infielder in the 1980s and currently the team's first-base coach, remembered Radomski.
"He was a clubhouse kid, one of several, one of the kids that were there," Johnson said before the Mets played at Washington on Friday night.
Former Mets pitcher Ron Darling, now a team broadcaster, said he didn't remember Radomski.
Mets spokesman Jay Horwitz said equipment manager Charlie Samuels would not be available for comment.
"We were surprised and disappointed to learn of the guilty plea today," the Mets said in a statement. "The conduct in question is diametrically opposed to the values and standards of the Mets organization and our owners.
"We are and always have been adamantly opposed to the use of performance-enhancing drugs and continue to support Major League Baseball's efforts to eradicate any such use in our game," the team said.