"We... are ready for practical cooperation with those countries which are part of the coalition and are ready to develop with them such forms of coordination that of course would respect Syria's sovereignty and the prerogatives of the Syrian leadership," Lavrov said in an interview with state-run Radio of Russia.
"I am convinced that such forms can be found if we take a pragmatic approach."
Russia first launched air strikes on Syria in September at the request of its long-standing ally President Bashar al-Assad, while a US-led coalition of countries opposed to the Syrian strongman is conducting a separate air campaign against IS.
In the aftermath of the Paris attacks on Friday, French President Francois Hollande called this week for a broad anti-IS coalition, echoing an earlier call made by Russian strongman Vladimir Putin made at the UN General Assembly in September.
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Hollande said he would next week discuss his proposal with US President Barack Obama and Putin, who has ordered his navy in the Mediterranean to establish contact with its French counterparts and work together "as allies".
Putin has been seeking to capitalise on shifting dynamics in the West following the Paris carnage and the bombing of a Russian passenger plane over Sinai in October, arguing that Russia and the West should unite against a common enemy.
Lavrov said he first detected a change in the Western position after Putin called for a broad coalition to fight the IS jihadists in Syria.
"Our Western partners realised the lack of prospects for the approach that many of them had taken."
On Wednesday Russia submitted a revised draft UN resolution on fighting the IS group that France said could be partially included in its own Security Council proposal.