"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.
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".
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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.
"Right now sensible politicians are putting secondary things aside and understand that it's necessary to focus attention on the priority: to prevent efforts by ISIL to conquer positions on the huge territory on Earth," he said, using another acronym for IS.
Lavrov reiterated Russia's traditional stance that Assad protected the interests of "a significant part of Syrian society" therefore it would not be possible to reach a settlement "without his participation."
He also praised signs of rapprochement between Russia and the West following months of tensions over Ukraine. "Our Western partners have put some formats on ice," he said, referring to venues such as the NATO-Russia Council.