The report cited opposition activists and US and foreign officials.
Obama administration officials emphasized the United States is not supplying or funding the lethal material, which includes antitank weapons, the report said.
Instead, they said, the administration has expanded contacts with opposition military forces to provide the Gulf nations with assessments of rebel credibility and command-and-control infrastructure, the Post said.
"We are increasing our non-lethal assistance to the Syrian opposition, and we continue to coordinate our efforts with friends and allies in the region and beyond in order to have the biggest impact on what we are collectively doing," said a senior State Department official, one of several US and foreign government officials who discussed the evolving effort on condition of anonymity, the Post reported.
US contacts with the opposition forces and the information-sharing with Gulf nations mark a shift in Obama administration policy as hopes dim for a political solution to the Syrian crisis, the Post said.