In exchange, Putin will expel the Iranians and their supporters from Syria, thus granting Netanyahu a historic victory.
The Israeli military said on Wednesday that it had shot down a drone from Syria that had entered its airspace.
A general view of refugee tents erected in Syria near the Israeli borderline as it seen from the Israeli-occupied Golan Heights, Israel July 3, 2018.
Iran is backing Syrian President Bashar al-Assad in the war, as is Russian Federation.
Israeli military spokesman Lt. Col. Jonathan Conricus said the drone was constantly monitored and that it traveled about 10 kilometers (6.2 miles) inside Israeli territory.
"We are still looking into why it crossed - whether it was on a military mission and crossed on objective, or it strayed", he said, while adding that the latter scenario was "not common".
Israel has been on high alert as Damascus forces advance on rebels in the vicinity of the Golan, much of which Israel captured from Syria in 1967 and annexed in a move not recognised internationally. Israel worries that Assad could let his Iranian and Hezbollah allies gain a foothold near Israeli lines.
Responding to a reporter's question if Israel would establish some kind of relations with Syria, Lieberman responded: "Our assessment is that we are far from that, but we do not rule out anything".
This trade, as reported by the Israeli press, would have Netanyahu offering to see Russian Federation given full relief from US-imposed sanctions in return for Russian Federation expelling Iranian military from Syria.
"We chose to bring with us two wonderful children who are bravely fighting cancer: Mika, whom my wife and I have known for nine years, and Alon, whose parents emigrated from Russian Federation and who likes soccer very much".
However, Lieberman appeared to signal acknowledgment that Assad would regain control of the Syrian side of the Golan. The United Nations last month renewed the mandate of its Golan observer force UNDOF and on Wednesday called on all parties to abide by the 44-year-old armistice arrangements.
Israel has warned Iran, which is allied with the Syrian government, against building up a military presence on its doorstep. Netanyahu's government has made clear it would not now cede the Golan and has been lobbying for USA recognition of Israel's claim of sovereignty there.
Israel fired a Patriot missile at an unmanned drone that entered its airspace from Syria on Wednesday, the military said, warning it would not tolerate such infiltrations, which have occurred several times over the past year. A Syrian commander said the drone was engaged in local operations. Israel and Russian Federation have set up a coordination mechanism over Syrian airspace to avoid an inadvertent clash between their forces.