Correspondent Matthew Cooper said he had told a grand jury last week that Rove told him the woman worked at the "agency", or CIA, on weapons of mass destruction issues and ended the call by saying, "I've already said too much."
He said Rove did not disclose the woman's name, Valerie Plame, but told him if that information was de-classified, it would cast doubt on the credibility of her husband, former diplomat Joseph Wilson.
Wilson had charged the Bush administration with exaggerating the threat of Iraqi weapons of mass destruction programmes in making its case for war.
"So, did Rove leak Plame's name to me, or tell me she was covert? No. Was it through my conversation with Rove that I learned for the first time that Wilson's wife worked at the CIA and might have been responsible for sending him? Yes. Did Rove say that she worked at the 'agency' on 'WMD'? Yes," Cooper wrote in Time's current edition.
"When he said things would be de-classified soon, was that itself impermissible? I don't know. Is any of this a crime? Beats me," Cooper wrote.
"Was it through my conversation with Rove that I learned for the first time that Wilson's wife worked at the CIA and might have been responsible for sending him? Yes"
Mathew Cooper, Time reporter
To intentionally reveal a covert CIA agent's identity in public is a federal crime in the United States.
Cooper also wrote that he was not certain what Rove meant by commenting he had already said too much.
Cooper testified on his conversations with Rove under court order before the grand jury to avoid going to jail and had received a last-minute waiver from Rove allowing him to break a confidentiality pledge. New York Times reporter Judith Miller was jailed for refusing to testify.
A federal prosecutor is investigating whether any government officials broke laws against exposing the identity of a covert CIA agent.
Columnist Robert Novak first revealed Plame's identity in July 2003, citing two administration officials, shortly after Wilson published an opinion piece in the New York Times that accused the administration of twisting intelligence on Iraq.
Wilson wrote that on a 2002 mission, funded by the CIA, he was unable to substantiate allegations that Iraq had tried to buy nuclear materials from Niger, as the White House asserted.
Cooper also reported on Plame's identity, attributing the information to Novak's column and administration officials, in a piece on Time's website shortly after Novak's column.
Wilson says the Bush administration leaked his wife's identity in retaliation for his article; Rove's lawyer said the aide had done nothing wrong and was not a target of the investigation. Other defenders have said Rove is the victim of a smear campaign.
Ex-diplomat Wilson (L) rejected
an Iraq-Niger nuclear link
US President George Bush has said he would fire anyone responsible for the leak but said last week he would withhold judgment on Rove's role pending the investigation.
Cooper also wrote in Time that in previous testimony to the grand jury he had discussed Wilson and his wife with Lewis "Scooter" Libby, a senior aide to Vice-President Dick Cheney.
He said he asked Libby whether he had heard anything about Wilson's wife sending her husband to Niger, and Libby replied, "Yeah, I've heard that, too."
Rove had used the same language in discussing the issue with Novak, according to media reports.