The former Daily Mirror editor told The New York Times it had been "a painful period" for the show, which has suffered lacklustre ratings.
CNN's audience had tired of hearing a Briton weigh in on American cultural issues, he said.
Mr Morgan said he was in discussions with CNN about a new role at the channel following the end of the show, probably in March.
The 48-year-old replaced veteran host Larry King three years ago and interviewed statesman and celebrities, including ex-President Bill Clinton, and financier Warren Buffett. Oprah Winfrey was his first guest.
But it was his outspoken remarks about gun ownership that have garnered most attention in recent months.
"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," he told the New York Times.
He said that he would like to do fewer appearances that have more impact.
Interviews with major celebrities and powerful figures, would be "better suited to what I do well", he said.
CNN did not comment on Morgan's future with the channel.
Earlier this month it emerged that Mr Morgan had been questioned by police under caution over alleged phone hacking at Mirror Group Newspapers.
He has always denied any involvement in hacking.
Prior to his move into TV, Mr Morgan was editor at the Daily Mirror newspaper and was sacked in 2004 after the paper published faked photos of British troops abusing Iraqi prisoners.
He went on to become a judge on Britain's Got Talent before joining CNN.
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