To take down the so-called Islamic State in Syria, the influential former head of the CIA wants to co-opt jihadists from America's arch foe.

Members of al Qaeda's branch in Syria have a surprising advocate in the corridors of American power: retired Army general and former CIA Director David Petraeus.

The former commander of U.S. forces in Iraq and Afghanistan has been quietly urging U.S. officials to consider using so-called moderate members of al Qaeda's Nusra Front to fight ISIS in Syria, four sources familiar with the conversations, including one person who spoke to Petraeus directly, told The Daily Beast.

The heart of the idea stems from Petraeus's experience in Iraq in 2007, when as part of a broader strategy to defeat an Islamist insurgency the U.S. persuaded Sunni militias to stop fighting with al Qaeda and to work with the American military.

The tactic worked, at least temporarily. But al Qaeda in Iraq was later reborn as ISIS, and has become the sworn enemy of its parent organization. Now, Petraeus is returning to his old play, advocating a strategy of co-opting rank-and-file members of al Nusra, particularly those who don't necessarily share all of core al Qaeda's Islamist philosophy.

However, Petraeus's play, if executed, could be enormously controversial. The American war on terror began with an al Qaeda attack on 9/11, of course. The idea that the U.S. would, 14 years later, work with elements of al Qaeda's Syrian branch was an irony too tough to stomach for most U.S. officials interviewed by The Daily Beast. They found Petraeus's notion politically toxic, near-impossible to execute, and strategically risky.