They are allegations the Minnesota Vikings running back's lawyer says were unfounded and more than a year old.
KHOU cited text messages that reportedly include a photo of the son with an apparent head wound covered by bandages.
Peterson was indicted by a grand jury on charges of reckless or negligent injury to a child on Friday. The prosecution in the ongoing case was aware of the June 2013 incident, a source familiar with the case told ESPN NFL Insider Adam Schefter.
Peterson, who apologized in a statement Monday for "the hurt I have brought to my child," also said he will testify in court that he did not intend to harm his son and said he is "without a doubt, not a child abuser."
The Houston TV station reported that the mother of the 4-year-old -- who is different from the mother of the child he stands charged with abusing -- filed a report with Child Protective Services, but no charges were brought.
Peterson attorney Rusty Hardin said in a statement that the accusation was more than a year old and that "authorities took no action."
"An adult witness admittedly insists Adrian did nothing inappropriate with his son," Hardin said in the statement to media.
The Vikings released a statement Monday night, saying they would "defer any further questions" from the media regarding the accusations to Hardin.
"As part of the information we have gathered throughout this process, we were made aware of an allegation from 2013 in which authorities took no action against Adrian," the Vikings said in the news release.
The reported text exchange was as follows, according to KHOU-TV:
Mother: "What happened to his head?"
Peterson: "Hit his head on the Carseat."
Mother: "How does that happen, he got a whoopin in the car."
Peterson: "I felt so bad. But he did it his self."
According to the report, Peterson then goes on to say he was disciplining his son for cursing at a sibling, though how specifically the child was wounded wasn't made clear.
Mother: "What did you hit him with?"
Peterson never directly answered, the report said, but later replied: "Be still n take ya whooping he would have saved the scare [scar]. He aight [all right]."
When asked about the 2013 accusation, Peterson's father, Nelson, said, "I haven't seen that report. I haven't heard any allegations."
Peterson has faced heavy criticism for his use of a so-called switch to discipline the other son, but the running back said in the statement released Monday that he "never imagined being in a position where the world is judging my parenting skills or calling me a child abuser because of the discipline I administered to my son."
The Vikings deactivated Peterson for Sunday's game against the New England Patriots but announced in a statement on Monday that he will play this weekend against the New Orleans Saints, adding they will let the legal process play out before deciding on further action. The NFL's only comment came on Saturday, when spokesman Brian McCarthy said the league will review Peterson's case "under the NFL's personal conduct policy."
The league considers the situation regarding Peterson to be under review, specifically by former New York prosecutor Lisa Friel, whom the NFL hired as a special consultant Monday as part of its social responsibility division, a league source told ESPN's Ed Werder.
Peterson is scheduled to enter a plea at an Oct. 8 hearing in Conroe, Texas, after his indictment for reckless or negligent injury to a child. Peterson faces up to two years in prison and a $10,000 fine if found guilty.
Information from ESPN.com's Ben Goessling and The Associated Press was used in this report.