David Cameron announced the public inquiry in July 2011, and is now reportedly expected to appear before it himselfCopyright: Peter MacDiarmid/PA
The Leveson inquiry is due to run a third module looking at politicians and the press later this year, but a spokesman for the inquiry declined to comment on whether Cameron would be called.
A Downing Street spokesperson said it has not yet received a request but that if the prime minister was called, he would attend.
The Times article today claimed that a source "close to the inquiry" was said to be "99.9 per cent certain" Cameron would be summoned to appear.
"Gordon Brown, the former prime minister, and Ed Miliband, the Labour leader, are also expected to be called to give evidence during the section of the inquiry considering relationships between press and politicians," the Times reports, but added that "a final decision on which politicians to invite had not yet been made".
It was David Cameron who officially announced the public inquiry into the "culture, ethics and practices of the British press" in July last year.
Later the same day reports emerged that Cameron's former director of communications, Andy Coulson, also former editor of the News of the World, had been arrested in connection to phone hacking and corruption allegations. He was later released on bail. Coulson has always denied any knowledge of wrongdoing at the now-closed newspaper.
At the July press conference announcing the inquiry Cameron responded to questions about his decision to hire Coulson, saying he had sought assurances from the former tabloid editor and adding that "the decision to hire him was mine and mine alone".
"I'm not hiding from the decision I made. He said he didn't know what was happening and I though it was right to give him a second chance ... People will make their own judgement."
Today's Times article reports that this decision is one topic Cameron is likely to face further questions on, should he appear later this year.