The possible cooperation comes even as top administration officials publicly criticize Moscow's own military actions in the country.
Under the proposed plan, the U.S. military and Russian Air Force would launch joint airstrikes against the al Qaeda-linked Jabhat al-Nusra, which is primarily fighting regime forces.
In exchange for deepening the military cooperation, Russia would halt its attacks on U.S.-backed rebels and other groups the U.S. does not consider terrorists, and agree to pressure Assad -- a close Russian ally -- to stop them as well.
Several U.S. officials familiar with the deliberations were highly skeptical Moscow would end up making good on such a deal, however.
The proposed plan, first reported
by The Washington Post, has been the product of intense interagency debate, the officials said. The Post reported the text of the plan has been sent to Moscow, but two other senior officials, speaking on condition of anonymity, said no final decisions have been made.
While he declined to discuss specific details of the proposed partnership, State Department spokesman John Kirby on Thursday acknowledged the effort to coordinate more closely with Russia
"We have been clear about Russia's obligations to ensure regime compliance with the cessation of hostilities," Kirby said. "We have also been clear about the danger posed by al Qaeda in Syria to our own national security. We are looking at a number of measures to address both of these issues."
While officials said the plan has the support of Secretary of State John Kerry, other top administration officials, including Defense Secretary Ash Carter, are said to be wary of deepening cooperation with Russia.
On Thursday, Carter spoke about Russia's unhelpful presence in Syria but said there was the potential for cooperation if Moscow stepped up its strikes against ISIS and helped move the political process for resolving the Syrian civil war forward.
"If the Russians would do the right thing in Syria -- and that's an important condition -- as in all cases with Russia, we're willing to work with them," Carter said.
An agreement with Russia to stop targeting moderate opposition forces could prove useful as the U.S. helps a coalition of Syrian Arab and Kurdish rebels to advance on ISIS self-proclaimed capital of Raqqa, something Carter said Washington was "very eager" to see happen "as soon as possible."
"Those are the forces that we are going to position to ... envelop and collapse ISIL's control of Raqqa," Carter said, using another acronym for the terror group.
Moscow has justified its airstrikes against moderate opposition forces by saying they have been entangled with al-Nursa and are not identifiable. The U.S. has pledged to try and separate the moderate rebels from al-Nusra fighters, but has often been unable to do so.
Russia's Defense Ministry hinted at the problem and the prospect of cooperation between Washington and Moscow earlier this month, saying Russia had suggested "compiling a joint map with actual information about location of forces active in Syria," but that no progress had been made toward that end.
The decision to deepen military cooperation is surprising, given the Obama administration's public criticism of Russia's role in Syria as both a cessation of hostilities negotiated in February and efforts to reach a political settlement in the war-torn country are on the verge of collapse.
Russia insists it has been targeting ISIS forces, but the majority of its airstrikes have been against U.S.-backed rebels battling Assad's forces, according to the U.S.
Kerry recently threatened a "Plan B" to increase arms to Syrian rebels if Russia and Assad did not change tactics and stop targeting moderate opposition groups supported by the U.S. and its European and Arab partners.
Earlier this month in Oslo, a visibly frustrated Kerry complained that Russia and the Assad regime were violating the February ceasefire agreement and stonewalling the delivery of desperately needed humanitarian aid.
"Russia needs to understand that our patience is not infinite," Kerry said. "In fact, it is very limited with whether or not Assad is going to be held accountable."
Troubled by the lack of leverage over both Russia and Assad, 51 U.S. diplomats sent a dissent memo to the State Department earlier this month calling for military action against Assad. The memo argued that neither Assad nor Russia have taken past ceasefires and negotiations seriously and suggested a more robust military approach was needed to force political change in Syria.
Kerry himself has advocated a more muscular U.S. military posture in Syria to put pressure on Russia and force Assad to negotiate a political settlement.
But even as it debates deeper military cooperation, the administration seems to be hedging its bets. Several senior administration officials told CNN earlier this week the administration was discussing possibly declaring the cessation of hostilities over and ending its cooperation with Russia if Moscow continued to violate the ceasefire and block the flow humanitarian aid.
But, at least for now, senior administration officials say the White House has concluded there is no alternative in Syria to trying to work with Russia, while attempting to keep the violence to a minimum.
On Wednesday, CIA Director John Brennan told an audience at the Council on Foreign Relations that Russia was violating the cessation of hostilities and that Assad was in a stronger position than a year ago because of Moscow's help. But he said he believed Russia was determined to "crush" terrorist groups like Jabhat al-Nusra.
And he acknowledged there was "no way forward on the political front without active Russian cooperation."