An MP from the Russian parliament, Igor Morozov, suggested that Turkish President Recep Tayyip Erdogan could offer Russia use of the airbase, which is currently used by NATO and is home to around 50 US nuclear warheads, Middle East Eye reported.
But a move for Russians to use Incirlik, based in the East of the country, would be highly controversial as Russia and NATO have been at odds over a number of issues, including Syria and the Ukraine.
"Turkey can provide the Incirlik base to the Russian Aerospace Forces for its use in counterterrorism operations in Syria. This can become a logical continuation of Turkish President Erdogan’s step toward Russia," Morozov told RIA Novosti.
Senator Viktor Ozerov, a member of Russia's Federation Council Defence and Security Committee, also suggested that use of the airbase could a gesture signaling the strengthening ties between the two countries.
Erdogan visited Moscow in early August to meet with Russian President Vladimir Putin and attempt to mend ties between the two countries, which became severely strained after the shooting down of a Russia fighter jet in November 2015.
"It is not guaranteed that Russia needs Incirlik, but such a decision can be regarded as Turkey's real readiness to cooperate with Russia in the fight against terrorism in Syria, and not just pay lip service," Ozerov said, according to the Russian Sputnik website.
Western analysts have raised concerns over the security of US warheads in the wake of the failed coup of 15 July, and the realignment toward Russia could add to NATO fears over its position in Turkey.
On Wednesday, Ibrahim Karagul, editor of the right-wing Yeni Safak newspaper, tweeted that Turkey should "take control" of the nuclear weapons in Incirlik.
"The nukes in Incirlik must be handed over to Turkey," he wrote. "Or else, Turkey should take control of them."
The suggestion comes as Russia has just started to use an Iranian airbase to strike targets in Syria, the first time Iran has given permission for a foreign power to use its territory for military operations since the 1979 Islamic revolution.
Russia's Defence Ministry said that SU-34 fighter bombers flying from Iran's Hamadan air base had struck ISIL targets in Syria's Deir Ezzur province on Wednesday, destroying two command posts and killing more than 150 militants.
Moscow first used Iran as a base to launch air strikes in Syria on Tuesday, deepening its involvement in the five-year-old Syrian civil war.
Washington called the move "unfortunate" and said on Tuesday it was looking into whether Russia's move had violated UN Security Council resolution 2231, which prohibits the supply, sale and transfer of combat aircraft to Iran.
Russian Foreign Minister Sergei Lavrov said on Wednesday there were no grounds to suggest Russia had violated the resolution, saying it was not supplying Iran with aircraft.
"These aircraft are being used by Russia's air force with Iran's agreement as a part of an anti-terrorist operation at the request of Syria's leadership," Lavrov told a Moscow news conference, after holding talks with Murray McCully, New Zealand's foreign minister.
Russia's use of the Iranian air base comes amid intense fighting for the Syrian city of Aleppo, where militatnts are battling Syrian government forces backed by the Russian military, and as Moscow and Washington are working towards a deal on Syria that could see them cooperate more closely.
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