WASHINGTON—Russia is taking advantage of opaque corporate-registration laws, permissive tax environments and uneven anticorruption practices to expand its economic footprint in certain Western Europe nations, according to a report to be released Monday.

The report by the nonpartisan Center for Strategic and International Studies think tank describes three countries—Austria, Italy and the Netherlands—as “enablers” whose financial and political systems have unwittingly or wittingly allowed the Kremlin to flex its economic and...