Colon, who has been married to his wife, Rosanna, for 21 years, was sued one year ago by 38-year-old Alexandra Santos, who alleges the 42-year-old pitcher hasn't paid child support for two children he fathered with her.
The suit, according to the Post, was filed as Anonymous v. Anonymous, but because Colon represented himself at one point, he is listed as an attorney in the case.
The newspaper reported that documents in the case are sealed and that Colon and Santos signed a confidentiality agreement last month. The sides are due to be in court again in June.
Colon has four boys with his wife and has not publicly acknowledged the 8-year-old son and 7-year-old daughter Santos alleges he fathered.
Rosanna Colon, contacted by the Post, said she was aware of the lawsuit and the claims that her husband has other children but otherwise declined comment.
Bartolo Colon, the oldest active player in the majors, is making $7.25 million this season on a one-year contract. By the end of this season, he will have made more than $101 million in his 19-year career.
"Mr. Colon obviously is a very talented baseball player and he earns a significant income, and we believe that his children should share in the lifestyle they would have enjoyed had their parents remained together," Evan Schein, the attorney who represents Santos, told the Post.
The newspaper reported that Colon's attorney didn't return multiple messages left for him.
Colon started Wednesday night against the Washington Nationals but did not pitch well. He was removed with two outs in the fifth inning with the Mets trailing 3-1, having allowed five hits and five walks. The Mets went on to lose 7-1.
Colon insisted the Post report was not a distraction.
"When I'm here doing my job, nothing else affects me," he said through a translator. "I have nothing to add to that. I don't care to talk about my personal stuff."
Colon has become a celebrated player in baseball because of his 5-foot-11, 285-pound frame and his comical at-bats and adventures on the bases. He made national headlines May 7 when he hit his first home run, becoming at 42 years, 349 days the oldest player to hit his first career homer.
Topps sold 8,826 trading cards with a picture of his home run in a 24-hour period, a record for the company.
Colon, through Wasserman, the agency that represents him, filed for the trademark to "Big Sexy" on April 19, according to a record from the U.S. Patent and Trademark Office. Colon intended to use the trademark on athletic apparel, including T-shirts, pants, shorts and hats.
This week, he forged a partnership with limited edition T-shirt maker Represent to sell a "Bartbino" shirt, a reference to one of Babe Ruth's nicknames, "Bambino."
ESPN's Darren Rovell and The Associated Press contributed to this report.