But Russia, one of Assad's few supporters, has warned that any move to supply rebel forces, primarily the secular Free Syrian Army, will be a major breach of international law.
Moscow has repeatedly blocked U.N. Security Council action that could clear the way for international military intervention. Russia has also provided large amounts of heavy weapons, including helicopter gunships and missiles, to Assad's military and security forces since the Syrian civil war began in March 2011.
After meeting in London with British Foreign Secretary William Hague Wednesday, Russian Foreign Minister Sergei Lavrov raised the specter of Western-supplied weapons falling into the hands of the Islamist groups who are fighting to topple Assad's minority regime.
But one of the presumed objectives of arming the FSA and other non-Islamist groups is to prevent the Islamist forces -- spearheaded by the increasingly powerful jihadist group Jabhat al-Nusra, which Washington deems a terrorist organization -- from elbowing them aside and establishing an Islamist-dominated regime in Damascus.
In recent weeks, the U.S. administration of President Barack Obama has been moving toward a major shift in policy concerning Syria by providing rebels with equipment such as armored personnel carriers, body armor and possibly military training as well.
Amid what appears to be a significant broadening of Washington's "non-lethal support" for insurgent forces in Syria, U.S. Special Forces were reported by Britain's Guardian newspaper Friday to be training "secular elements of the Syrian opposition" in Jordan, along with British and French instructors "as a bulwark against Islamic extremism."
The German newsmagazine Der Spiegel reported two days later that the Americans were engaged in "full-scale training" for fighters from the FSA, the largest non-Islamic rebel force in Syria.
Der Spiegel said the aim of the Jordan operation is to train up to 10,000 fighters who will form a dozen or so combat brigades.
On paper at least, that could be a formidable non-Islamist force that would be a pro-Western bulwark against any jihadist effort to dominate a successor regime in Damascus if Assad is toppled.
The training operation, which reportedly began on a smaller scale in 2012, clearly has the support of Jordan's intelligence service, a key and valued ally of U.S. and British intelligence agencies in the battle against jihadist forces.
Jordan, Syria's southern neighbor, is alarmed at the prospect of a jihadist regime emerging in Damascus that could threaten the pro-Western Hashemite kingdom.
The resource-poor desert country is under growing strain from a major refugee problem. Some 400,000 Syrians have sought shelter there and Amman fears that could rise to 1 million in the weeks ahead as the war, 2 years old Friday, intensifies.
The shift in U.S., British and French policy regarding the Syrian conflict has come at a time when it appears the jihadist forces fighting Assad are making major gains, primarily in northern and northeastern Syria.
These are outstripping the so-called moderate forces of the FSA and the umbrella Syrian National Council.
The idea now seems to be to establish a rebel zone in southern Syria, above the border with Jordan and manned by pro-Western forces, to provide a counterweight to the rebel-held zone in northern Syria dominated by Islamists.
All this is far short of direct military intervention, such as mounting airstrikes and naval gunfire as NATO forces did during the eight-month war against Gadhafi that ended with his death Oct. 20, 2011.
But it's clear there's growing alarm at the swelling power of the jihadist forces in Syria, and the prospect of an Islamist regime in Damascus.
In particular, the Western powers want to stamp out Iran's influence in the Levant, isolate Tehran, already battered by Western sanctions over its nuclear program, and eliminate Hezbollah on Israel's northern border.
The British and French say they're prepared to bypass an EU arms embargo on Syria as events unfold.
How far the Obama administration is prepared to go isn't clear.
But with the prospect bleak for a diplomatic solution to the Syrian crisis, the arrival of John Kerry as U.S. secretary of state could signal a new policy in Washington.