It has long been evident to observers of the right-wing Fox News channel that its creator and current chairman, Roger Ailes, likes to play kingmaker within the Republican party. Why else would he have employed no fewer than five potential presidential candidates as his on-air contributors?

But until this moment it was not fully appreciated just how literally he takes the role. Courtesy of an old-fashioned scoop from that doyen of scoop-meisters, Bob "Watergate" Woodward of the Washington Post, we now know the extraordinary lengths the TV executive is prepared to go to influence the electoral process.

Woodward reveals that in 2011 Ailes dispatched a Fox News analyst to Afghanistan in a secret mission to try to convince the then-commander of US forces there, General David Petraeus, to enter the race for Republican presidential nomination. Had Petraeus not rebuffed the invitation, and agreed to run, Ailes himself was ready to stand down from his 16-year reign at America's dominant cable news network in order to manage Petraeus's presidential campaign.

Woodward further reveals that Rupert Murdoch, chairman of News Corporation which owns the Fox News network, would have been willing to fund the general's White House bid had he decided to stand.

The discussion behind Woodward's story takes place in the then-general's office in Kabul some time in early 2011, before Petraeus has accepted the job as CIA director from which he resigned last month in the wake of the scandal over his affair with his biographer. On one side of the table is Petraeus, on the other Kathleen McFarland, a Fox News national security analyst who is acting as Ailes's envoy.

McFarland begins by promising Petraeus absolute discretion, saying that Ailes's "deal with me was that I was only supposed to talk to you – and he is a little paranoid, so believe me." However, the 90-minute conversation was recorded, and a digital copy of it somehow made its way into Woodward's hands.

"I've got something to say to you directly from Roger Ailes," McFarland is captured saying on the recording that has been posted in edited form on the Washington Post website. "I'm not running," Petraeus snaps back.

McFarland, a Pentagon adviser to the Reagan administration, does not take no for an answer. The next time Petraeus is in New York, she says, he should come and "chat to Roger and Rupert Murdoch", to which Petraeus, for whom this conversation is clearly not the first of its kind, replies: "Rupert's after me as well."

"Tell him if I ever ran … " Petraeus laughingly says as the meeting is wrapping up. "I'd take him up on his offer. He said he would quit Fox."

McFarland says that "the big boss" would "bankroll" the campaign – a clear reference to Murdoch. "The big boss is bankrolling it. Roger's going to run it. And the rest of us are going to be your in-house."

The Fox News chief tried to make light of the recording in a telephone interview with Woodward on Monday. "It was more of a joke, a wiseass way I have," he said, before going on in time-honoured fashion to blame the messenger – in this case McFarland.

"She was way out of line. It's someone's fantasy to make me a kingmaker. It's not my job."

It may not be his job, but that appears never to have inhibited Ailes in the past. In 2010 Ailes paid five leading Republicans and potential presidential candidates to appear on Fox News - John Bolton, Newt Gingrich, Mike Huckabee, Sarah Palin and Rick Santorum.

As Gabriel Sherman, a New York magazine writer whose biography of Ailes will be published next year, pointed out in May 2011 http://nymag.com/news/media/roger-ailes-fox-news-2011-5/ , he also tried to persuade Chris Christie, the governor of New Jersey, to throw his hat in the Republican primary ring. As one party insider told Sherman: "You can't run for the Republican nomination without talking to Roger."

Ailes, who worked as a conservative political strategist before entering broadcasting, continues to have regular audiences with the two leading Republicans in Congress, John Boehner in the House and Mitch McConnell in the Senate. "Big boss" Murdoch also likes to dip his toes into Republican waters, authorising News Corp to give more than $2m in donations to pro-GOP organisations in the run-up to this year's presidential race.

In the end, of course, Petraeus remained true to his word and kept out of the 2012 election. Paradoxically, given more recent events, he told McFarland one reason he would not run was that "My wife would divorce me".

Ailes told Woodward that there was "zero chance" he would really have quit his job, as "the money is too good". With a salary of at least $21m a year, you can see his point.

But that was then. Will money be enough to hold back the Kingmaker when it comes to 2016?