Washington condemned Assad's conduct of the conflict, threatened air strikes after he was accused of targeting civilians with chemical weapons and has demanded he step down.
The United States is also supplying millions of dollars in "non-lethal" aid to some of the rebel groups fighting Assad's rule.
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"Option three is Assad wins," Hayden told the annual Jamestown Foundation conference of terror experts.
"And I must tell you at the moment, as ugly as it sounds, I'm kind of trending toward option three as the best out of three very, very ugly possible outcomes," he said.
The first possible outcome he cited was for ongoing conflict between ever more extreme Sunni and Shiite factions.
The rebel groups are dominated by Sunni Muslims, while Assad is generally backed by Syria's Alawite, Shiite and Christian minorities.
And the second outcome, which Hayden deemed the most likely, was the "dissolution of Syria" and the end of a single state within the borders defined by a 1916 treaty between the French and British empires.
"It means the end of the Sykes-Picot (Agreement), it sets in motion the dissolution of all the artificial states created after World War I," he said.
The British diplomat Mark Sykes and a French counterpart Francois Georges Picot divided the Middle East into zones of influence that later served as the frontiers of independent Arab states.
A breakdown in the century-old settlement could spread chaos in Lebanon, Jordan and Iraq, Hayden warned.
"I greatly fear the dissolution of the state. A de facto dissolution of Sykes-Picot," Hayden said.
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