CNN said today that the date of the final edition of Piers Morgan Live has yet to be decided.
Morgan replaced Larry King in the 9pm slot three years ago and has interviewed statesmen and celebrities - but his show has had lacklustre ratings.
The 48-year-old former tabloid editor 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 on the newspaper's website today.
"It's been a painful period and lately we have taken a bath in the ratings," he said.
Morgan added: "Look, I am a British guy debating American cultural issues, including guns, which has been very polarising, and there is no doubt that there are many in the audience who are tired of me banging on about it.
"That's run its course and Jeff and I have been talking for some time about different ways of using me."
CNN did not comment on Morgan's future with the channel.
Earlier this month, Morgan - former editor of the Daily Mirror - confirmed he had been questioned over claims of phone hacking.
He was interviewed under caution at the end of last year by officers investigating claims of illegal interception of voicemails by Mirror Group journalists.
The Mirror Group was brought into the phone-hacking investigation for the first time in March last year when detectives from Operation Weeting arrested four journalists in dawn raids.
Morgan - known for reducing guests to tears on his ITV show Life Stories - has said in the past that he believes he is the best at his job in Britain.
He said he rated Michael Parkinson but said he thought he was better than everyone else.
Asked in October last year whether he was now the best TV interviewer in Britain, Morgan boasted: ''Yes, because I don't think that my so-called rivals do what I do.
''I'm the only person who sits down with people on TV for two or three hours to truncate to a one-hour show. So I think I'm almost in a category of my own.''
Morgan told the Radio Times: ''I can't compete with Graham Norton for the comedy he brings and I think he's got a terrific show. Or Jonathan Ross. Or Alan Carr. They're all entertainers and comedians, really.
''They're not any of them particularly great interviewers. I don't think they profess to be. Parky could do both.''
Asked whether he would like to be the next Parky, Morgan replied: ''No. He might like to be the next Piers Morgan. I like Parky but he doesn't think anyone else could ever come anywhere close to being as good as him.''