He hosted BBC's "You Can't Fire Me, I'm Famous," and did interview shows and documentaries for ITV.
Morgan told The New York Times that his show lately has "taken a bath in the ratings" but that he and CNN President Jeff Zucker were discussing a new role for him at the channel. CNN's audience has tired of hearing a Brit weigh in American cultural issues, Morgan said in a story posted online Sunday.
Morgan's future with CNN is undetermined, the channel said.
Last fall, the already struggling "Piers Morgan Live" faced increased competition from a revised Fox News Channel lineup that included a strong new performer at 9 p.m. EST with Megyn Kelly's "The Kelly File."
Morgan served as editor of The Daily Mirror from 1995 to 2004. He has been questioned in connection with Britain's long-running phone hacking scandal, which has led to numerous arrests, resignations and the closure of Rupert Murdoch's News of the World tabloid.
Earlier this month, Morgan confirmed that he was interviewed in December by British police investigating the illegal interception of telephone voicemails. Morgan, who said he had given a previous witness statement, has consistently denied wrongdoing.