The United States has sent humanitarian aid to Syria but has declined requests for weapons by rebels fighting to overthrow the government of Syrian President Bashar al-Assad.
The White House rejected the Clinton-Petraeus proposal over concerns it could draw the United States into the Syrian conflict and the arms could fall into the wrong hands, the Times said, citing unnamed Obama administration officials.
The plan called for vetting rebels and arming a group of fighters with the assistance of some neighboring countries.
Some administration officials expected the issue to come up again after the November U.S. elections, but the plan apparently died after Petraeus resigned because of an extramarital affair and Clinton missed weeks of work with health issues, the Times said.
Clinton, who stepped down as secretary of state on Friday, declined in a recent interview with the Times to comment on her role in the debate over arming the rebels.
Outgoing Defense Secretary Leon Panetta was said by some officials to be sympathetic to the idea, the paper reported.
Petraeus and a spokesman for Panetta declined to comment, the Times said.
(Writing by Eric Beech; Editing by Peter Cooney)