Lagarde's two-day stay in Moscow -- her first official foreign trip outside the European Union -- will include talks on Monday with President Dmitry Medvedev and meetings at the finance ministry and the central bank.
The Kremlin said the European public debt crisis will dominate negotiations just as it had done at the recently concluded Group of 20 summit in Cannes.
Medvedev and Lagarde will also discuss "further steps on reforming the global financial system," the Kremlin said.
Resource-rich Russia has resisted offering direct assistance to Europe and instead preferred to funnel funds or other measures through the safer investment mechanisms made available by the IMF.
But Medvedev's top economic adviser said that even the extra funding being negotiated with Lagarde's agency would be limited to $10 billion -- a token figure when compared to the $100 billion being discussed with China.
Strong prices for Russia's energy exports have left Moscow in a prime position to make European investments that help revive important market demand.
Economists note however that the Russian government only has about $100 billion left in its special rainy-day fund after spending most of it on recovery measures from the 2008-2009 crisis.
The $520 billion in international reserves held by the central bank meanwhile are mostly invested in low-risk government bonds rather than the high-yield debt available from struggling nations such as Italy and Greece.
"If we ever see any eurozone bonds, the central will be a big buyer," said Alexei Moiseyev of VTB Capital in reference to a European funding option resisted in the past by Germany.
"But since this is unlikely, Russia's role in financing Europe's stabilisation will be limited to transactions conducted jointly with the IMF or with the countries themselves," Moiseyev wrote in a note.
Lagarde herself said at the G20 summit that her organisation could not directly help fill the new eurozone rescue fund -- known by its acronym EFSF -- because the IMF only strikes agreements with individual countries.
"If the EFSF is called upon to intervene in a particular country, the IMF can partner with the EFSF on the particular venture in which the EFSF is engaged," Lagarde told a G20 briefing on Friday.
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