The possible U-turn comes as Obama has no clear strategy to resolve the crisis and apparently shrinking options for speeding Syrian President Bashar Assad's exit, the newspaper said.
Obama rejected a proposal by four top national security officials who wanted to arm the rebels last fall.
Those officials were Defense Secretary Leon Panetta, Joint Chiefs of Staff Chairman Gen. Martin Dempsey, David Petraeus, the CIA director at the time, and Hillary Clinton, then the secretary of state.
The rift became public Feb. 7 when Panetta and Dempsey told the Senate Armed Services Committee they both supported the proposal brought to Obama in the fall but were rebuffed.
A question is whether Obama, surrounded by a new national security team -- including Secretary of State John Kerry and Chuck Hagel if he is confirmed as defense secretary -- would reach a different conclusion, the Times said.
"This is not a closed decision," a senior administration official told the newspaper. "As the situation evolves, as our confidence increases, we might revisit it."
U.S. officials told The Wall Street Journal after Panetta and Dempsey testified before the Senate panel, Obama shelved the idea because of lingering questions about which rebels could be trusted with the arms -- and whether the weapons could be used against civilians or Israeli and U.S. interests.
The New York Times reported those same concerns Tuesday.
The officials said Obama also questioned if arming the rebels would really help remove Assad, the Journal said. Obama also wondered if the weapons would add to civilian suffering, the officials said.
A U.S. official told the Journal at the time a CIA team of analysts had cast doubt on the benefits of arming the rebels.
The proposal was broached before the November election, officials said. Obama had campaigned on the theme that "the tide of war" was receding.
Vice President Joe Biden and national security adviser Thomas E. Donilon advised against the plan, the Times said.
Some administration officials expected the issue to be re-examined after the election. But when Petraeus resigned because of an extramarital affair and Clinton suffered a concussion, missing weeks of work, the issue was removed from consideration, the Times said.
The proposal called for the United States to vet the rebel groups and train fighters supplied with weapons, with the help of a neighboring state.
The risky plan offered the potential reward of creating Syrian allies the United States could work with during the conflict and after Assad's eventual removal, the Times said.
While the White House focuses on the risks of providing weapons, other nations -- including Russia, Iran and Lebanon's Shiite Islamic military group and political party Hezbollah provide weapons and other assistance to the Assad regime, the Times said.
Rebel fighters tied to al-Qaida receive financial aid and other support from Middle East backers, the newspaper said.