The deal is backed by US Secretary of State John Kerry and has been personally approved by US President Barack Obama, the publication added, noting that the United States has in return requested Russia to pressure the Syrian government to stop carrying out strikes against groups not considered terrorist by the United States.
Given the difficulties involved in identifying separate rebel groups and separating al-Nusra Front from other groups, the Obama administration proposed designating entire geographic areas as off-limits for the Syrian air force, according to the Washington source.
The US Department of State declined on Thursday to discuss ongoing diplomatic conversations with Russia.
John Kirby told Sputnik that the State Department "will not speak to the details of any ongoing internal or diplomatic conversations."
Russia has been calling on the United States to cooperate in Syria since the start of the Russian counter-terrorist aerial campaign in September. Russian President Vladimir Putin has called for a broad anti-terrorist coalition as well as stressing the need for establishing regular contacts between US and Russian defense ministries.