The PSNI confirmed it was reviewing what he said.
Mr Brolly made the remarks to Virgin Media Sport, and described feeling “ecstatic” after donating a kidney to a stranger.
“Then I hit the wall shortly after that,” he said. “I think for years I had blocked out childhood – I couldn’t even remember childhood properly.
“I realised soon afterwards that the reason I’d given the kidney was to, I think, atone for the taking of human life by people close to me and to sort of somehow make amends for that.”
Mr Brolly did not elaborate on his remarks.
However, David Temple, whose 16-year-old brother, William, was killed at Claudy, Co Derry, along with eight others, branded the comments “disgraceful”.
Mr Brolly did not specify what he was referring to and whether his remarks were in any way referring to the Claudy bombing.
The PSNI detained four people in connection with the bombing in 2005, including Mr Brolly’s late father Francie, a Sinn Féin MLA at the time. They were released without charge the next day. All denied involvement.
Francie Brolly subsequently began legal action against the PSNI over his arrest, but he did not proceed with his case.
Mr Temple said: “My family and those of all the other victims have never got justice and are still seeking answers. Claudy still is very controversial.
“Joe Brolly can’t just release wee bits of information here and there, it’s not fair on the families.”
Mr Brolly was contacted for comment.
The PSNI said: “We are aware of comments made in the interview and of subsequent press reporting in relation to those comments and will review the content of the interview.”
Kenny Donaldson, of Innocent Victims United, urged police to examine the video in order to “establish if there are grounds for Mr Brolly
to be spoken to on these matters”.
In September, Mr Temple’s family and those of victims David Miller (60) and James McClelland (64) settled legal action against the police and the Northern Ireland Office over the atrocity.
Settlements were agreed without an admission of liability from either.
In 2010, a Police Ombudsman’s report found that Catholic priest Father James Chesney, who died in 1980, was a suspect in the bombing and was moved by the c
hurch to a parish in the Republic a year after the attack.
The report said the police, British state and the Catholic Church had covered up his suspected role.