"I think it would be a legitimate thing to do," Clinton told CNBC in an interview that aired Friday. He was interviewed alongside Mati Kochavi, a cybersecurity entrepreneur.
But Clinton added that if such an agency were ever created, it would have to be "totally transparent" about where its funding came from and would have to be independent.
"Let's just say the U.S. did it. It would have to be an independent federal agency that no president could countermand or anything else because people wouldn't think you were just censoring the news and giving a different falsehood out," he said.
"That is, it would be like, I don't know, National Public Radio or BBC or something like that, except it would have to be really independent and they would not express opinions, and their mandate would be narrowly confined to identifying relevant factual errors," he said.
Clinton said the agency would have to have citations so it could be checked in case it made a mistake.
"Somebody needs to be doing it, and maybe it's a worthy expenditure of taxpayer money," he said. "But if it's a government agency in a traditional sense, it would have no credibility whatever, particularly with a lot of the people who are most active on the Internet."