Foreign Minister Ioannis Kasoulides said there was a "dialogue between the governments of Cyprus and Russia on the matter of facilities for humanitarian and emergency purposes".
He told reporters that France, which is also waging an air campaign in Syria, had "requested facilities for returning aircraft on operations so if there is an emergency situation they can land at Cyprus airports".
Cyprus was obliged by law to offer similar facilities to other countries in emergency situations, particularly when lives are at risk, Kasoulides said.
France is part of a US-led coalition that has been fighting the Islamic State group since last year but has intensified its operations following Paris attacks last month.
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Russia launched its air campaign in September in support of the regime of President Bashar al-Assad.
British warplanes, part of the US-led coalition, are already flying operations against IS in both Syria and Iraq from the RAF base of Akrotiri on the south coast of Cyprus.
War-torn Syria, where IS has its main stronghold in Raqa, is located only some 110 kilometres from the eastern Mediterranean island.