According to the paper's sources, a Saudi delegation shuttled between Moscow and Riyadh during the waning months of 2014 to pressure Russian President Vladimir Putin into changing his stance on Syria.
The Saudi monarchy is at odds with Assad, and is widely believed to be backing anti-government rebel groups there. Independent militia groups such as the violent Islamic State insurgency, are in control of large areas of the country.
Global oil prices started to nosedive last summer amid oversupply on the market. Saudi Arabia voted against a curb in oil output by the 12-nation OPEC cartel of world's largest oil producers.
But the New York Times cited Saudi officials as telling the United States following the talks in Moscow that they believed to have the upper hand in Russia due to their ability to reduce oil output and drive down oil prices.
The Russian economy is highly dependent on oil revenues and has slowed down in the past months following the low oil prices.
Russia's Foreign Minister Sergei Lavrov said after a November meeting with his Saudi counterpart in Moscow, that both parties agreed oil prices should be regulated by normal market conditions.