Later, the Tory maverick Nadine Dorries gave her list of four possible future Conservative leaders, only one of whom, the Education Secretary Michael Gove, is in the Cabinet. Two others Mr Afriyie and Jesse Norman are backbenchers, while London's Mayor, Boris Johnson, is not an MP. The Chancellor, George Osborne, was noticeably missing from her list.
The speculation began after three Tory-supporting Sunday newspapers reported a "well-organised" campaign to secure the leadership for Mr Afriyie, who was a frontbench spokesman for the Conservatives in opposition but was excluded from the government.
His backers say he has a life story that could give the Tories an appeal beyond their normal base of support, as the state-educated son of Ghanaian father and an English mother, and a self-made multi-millionaire.
Mr Afriyie said he almost choked on his breakfast cereal when he read the reports. He told Sky News: "I will never stand against David Cameron. I am 100 per cent supportive of David Cameron... There is no truth to any of it. We are working very hard to keep David Cameron secure, to make sure there is not a vacancy."
However, he also said he and his allies had talked about "the long-term future of the party", indicating that he sees himself as a candidate in a post-2015 leadership contest if the Tories lose the general election.
The promise not to stand against Mr Cameron is actually meaningless, because the rules of the Conservative Party, revised after the fall of Margaret Thatcher, do not permit a direct challenge to a Tory Prime Minister, who must be felled by a vote of no confidence before an election can be held to choose a successor. The risk of that happening to Mr Cameron while he is Prime Minister appears to be remote.
Ms Dorries, who is still not officially a Tory MP, having had the whip withdrawn over her high-profile appearance on reality television, came out as a potential Afriyie supporter. She told Sky: "He's a friend of mine and I do not believe for a second anyone close to Adam has leaked this story.
"He has got leadership potential however, winning the next election with David Cameron in 2015 is Adam's priority. It's a long term objective he has like Jesse Norman, like Boris Johnson, like Michael Gove."
The outbreak of speculation about the leadership came as a surprise after a week when Mr Cameron had soothed his critics on the Tory right with a speech setting out how he would call a referendum on Europe in the next Parliament, and a new opinion poll showing Labour's lead narrowing.