"Such an idea is lingering, but there is no decision about it as yet," the source said.
Analysts doubted that the plan would be adopted, saying it would be highly damaging for Russia's investment climate and would face opposition from major companies.
Earlier on Tuesday Russia's Kommersant newspaper reported that the Finance Ministry had prepared legal amendments that would bar state companies, as well as strategically important private firms.
The Finance Ministry declined to comment.
Under the proposals, all state-owned companies would be allowed to have accounts only at Russian state-owned banks, or at privately-owned Russian banks with capital of at least 16.5 billion roubles ($483 million), Kommersant reported.
The restrictions would also apply to privately-owned companies that were significant for Russia's defence or security, as defined by an existing law on foreign investment in strategic companies.