A source had told The Times that Lord Justice Leveson is "99.9% certain" to call the prime minister forward as part of his investigations into the role of the press and police in the phone hacking scandal.
A Downing Street spokesperson told PA: "A request has not yet been received. If asked, the prime minister would of course attend."
If called, Cameron would answer questions under oath about his relationships with journalists and media bosses, and may be asked about his decision to hire former News of the World editor Andy Coulson as his communications chief.
Coulson began work for Cameron in July 2007 when he was in opposition to the then-Labour government, but resigned in January 2011, saying that "continued coverage of events" during his tenure as News of the World editor prevented him from "[giving] the 110% needed".
The insider - who was not named by the paper but is said to be somebody who is "close" to the Leveson Inquiry - hinted that Cameron would be called after the next round of local elections in May.
The source said: "I can't see how you can look at the relationship between the press and politicians without talking to top politicians."
It is also believed that former prime minister Gordon Brown, who preceded Cameron in office, and the current leader of the opposition Ed Miliband will also be called forward to give evidence about their dealings with the press.
More news from the Leveson Inquiry:
> The Sun editor Dominic Mohan: 'We no longer use private investigators'
> Piers Morgan denies Daily Mirror ever hacked phones
> News of the World reporters defend the paper at Leveson Inquiry