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Morgan succeeded Larry King in the late night time slot three years ago, but his show has had lackluster ratings.
CNN said Sunday that the show's final airdate has yet to be determined.
Morgan is a former British tabloid editor who turned to television, including stints as a judge on NBC's America's Got Talent and a contestant on Celebrity Apprentice.
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 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.
CNN did not comment on Morgan's future with the channel.
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.
