The move comes as he prepares to go head-to-head with Gordon Brown if – as expected – the Chancellor takes over from Tony Blair later this year.
The move would be similar to that made in the mid-1990s when Blair brought in Alastair Campbell to steer Labour to power.
A senior source with close links to top Conservatives said: ‘This is an ongoing process that senior people in the party are talking about. The piece that’s missing for the party at the moment is building Cameron’s reputation among key editors and leader writers.’
The source added: ‘It’s a question of persuading a big-hitter to put their faith in the fact that Cameron might be the next prime minister.’
US-based BBC journalist Guto Harri is believed to be one name in the frame.
Harri, whose stint in New York ends shortly, said he was in ‘regular contact with senior Conservatives as part of [his] job’ but added: ‘I have no plans to become a PR man.’
Another name connected with the post is The Sun’s Trevor Kavanagh. PRWeek was unable to contact Kavanagh for comment.
Cameron’s current head of press George Eustice said there were no plans to appoint either man. Eustice would only say: ‘We may well expand the press office as we move closer to the general election.’