Instead of interest, which is prohibited on religious grounds, Islamic finance relies on banks charging service fees and depositors sharing in bank profits. Turkey is another country that is looking to expand in the sector.
"During a period of a practically total economic blockade from Europe and the U.S., our banks must find new ways to attract investment," said Dmitry Savelyev, who sits on the Duma's financial markets committee.
Western-imposed sanctions on Russian officials and large firms over the country's role in the Ukraine crisis have dried up access to international capital markets. A collapse in oil prices has further contributed to a slowdown in the economy, which is expected to contract by at least 3 percent this year.
The draft law must pass three readings in the Duma before it moves to the upper house and then to President Vladimir Putin's desk to be signed into law.
Lawmakers would have to pass further amendments in areas such as taxation before the sector can fully develop. The changes could take at least a year to be passed, experts say.
State development bank Vnesheconombank and VTB Bank, both hit by sanctions, have sought to build their Islamic finance know-how in a bid to develop new funding sources.
One impulse for the recent efforts is that Russia is looking to diversify its economic ties away from Western markets, said Linar Yakupov, the head of the Association of Regional Investment Agencies of the Russian Federation.
"This is where recent sanctions became a kind of catalyst, an extra push, to further look at the economic perspective in the relationship between Russia and OIC (Organisation of Islamic Cooperation) countries," he said in an interview in Bahrain.
Islamic finance could attract foreign investment and also mobilise funds from Russia's 20 million Muslims, Yakupov added.
Legislation is crucial to facilitating Islamic finance transactions which can attract double or triple tax duties as they require multiple transfers of underlying assets, moves which countries like Britain and Luxembourg have addressed.
"It is theoretically and technically possible for the government to prepare a law on Islamic banking, but it all depends on political will," said Murad Aliskerov, chief executive of LaRiba Finance, an Islamic financial company based in Russia's Dagestan republic.
"Islamic banks could have a huge social impact and act as an alternative to traditional banks."
A feasibility study is now under way between a consortium of Russian and Malaysian investors to create a standalone Islamic bank or an Islamic unit within a Russian lender, Yakupov said.
The study would be ready by September, allowing the sides to draw up concrete details for creating such an entity and assess which laws would have to be changed, he said.
Companies are also keen to explore Islamic bonds (sukuk) as alternative financing tools, with Russia's Tatarstan republic hosting an industry summit next month focused primarily on such instruments.
The impact could extend to former Soviet republics in central Asia. A proposal is being pushed to create a regional working group to coordinate Islamic finance efforts with countries such as Kazakhstan, Tajikistan and Kyrgyzstan.