AFP reports citing Israeli daily Haaretz.
Netanyahu "will travel to Moscow in the next two weeks and meet with President Vladimir Putin, " Haaretz posted on its website late on Friday, citing a senior Israeli official.
"Netanyahu and Putin will discuss the Russian arms sales to Syria, in particular the sale of advanced S-300 anti-aircraft missile systems," it said, adding that the premier would also seek to raise the Iranian nuclear issue.
Contacted by AFP on Saturday, Netanyahu's office declined to comment.
Israel twice last week carried out air strikes near Damascus, attacks a senior Israeli source said were aimed at preventing the transfer of sophisticated weapons to the Hezbollah, the powerful Lebanese Shiite group allied to Syria.
The Wall Street Journal reported on Wednesday that Israel had provided information to Washington about the imminent sale to Syria of Russian S-300 missile batteries, advanced ground-to-air weapons that can take out aircraft or guided missiles.
British Prime Minister David Cameron visited Putin at his Black Sea vacation home on Friday to talk strategy on the Syria crisis, days after top US and Russian diplomats agreed to work together on a solution to the conflict.
In a visit to Warsaw on Friday, Russian Foreign Minister Sergei Lavrov said Moscow was continuing to fulfil contracts by delivering military hardware to Syrian President Bashar al-Assad's regime in defiance of calls for a freeze.
"Russia has sold and signed contracts a long time ago, and is completing supplies of the equipment, which is anti-aircraft systems, according to the already signed contracts," he told reporters.
The West and Russia have been repeatedly at odds over the Syria conflict, with the United States and Europe accusing Moscow of seeking to prop up Assad and selling him arms.
The war in Syria has cost an estimated 70,000 lives and displaced millions of people, including hundreds of thousands who have fled to neighbouring countries.
Cameron's talks with Putin came amid concerns that Russia may be preparing to hand over to Syria sophisticated surface-to-air missiles, which would significantly strengthen its defences and complicate any foreign intervention.
US Secretary of State John Kerry has warned that any such sale would be "potentially destabilising" for the region.