Cameron, who became prime minister in 2010, ruled out seeking a third term in office before May's election when his Conservative Party won an unexpected parliamentary majority.
He said that he would like to serve a full second term until 2020 when a parliamentary election is due to be held.
However, an article in the Spectator, a right-leaning magazine closely aligned with the Conservative Party, said Cameron had chosen an earlier date for his departure.
"His closest allies in Downing Street have been told that he intends to announce he's leaving in the spring of 2019," the magazine's political editor wrote in an article.
This timetable was rejected by a Downing Street source. "The PM (prime minister) has been clear and unequivocal on this. He'll serve a full term, that's a matter of public record and that remains the case," the source said.
When Cameron announced he would only serve two terms, he said possible successors included Theresa May, the interior minister, London mayor Boris Johnson, and finance minister George Osborne.
The Spectator said Nicky Morgan, the education secretary, had indicated that she was considering running for the job, telling the magazine: "A lot of it will depend on family."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ