A proposal had been submitted to the Russian government and some foreign banks, including HSBC and Deutsche Bank, which have indicated they would like to have such negotiations, the Nikkei business daily said.
Deutsche Bank and HSBC both declined to comment.
The request was submitted by the Russian Association of Regional Banks, Anatoly Aksakov, president of the industry group, told the Nikkei in an interview.
The government would negotiate with foreign banks on behalf of the Russian lenders, and may include some repayment guarantees, if the proposal is accepted, the report said.
The euro fell sharply on the report, with the single European currency sliding more than 1 per cent against both the dollar and the yen.
"It has always been the case that what's bad for Russia is bad for the euro as well," said Jan Lambregts, head of research, Asia, with Rabobank Global Financial Markets in Hong Kong.
In addition to business ties between Europe and Russia, the ruble is tied to a euro-dollar basket.
Aksakov, a prominent banking lobbyist, was not available for comment on Tuesday.
Russian officials have so far made no remarks suggesting Russia may seek to postpone corporate debt.
"There is an obvious mismatch between a source of information and one-time financial consequences," a Russian government source, who declined to be identified, told Reuters.
Over the last six months, Russia has spent a third of its foreign exchange reserves, or about $200 billion, to ease downward pressure on its currency as the ruble was devalued to trade more in line with lower oil prices and slower economic activity.
The euro was down around 1.4 per cent at $1.2825 and off 0.8 per cent against the ruble at 46.2885.
"As was the case last week when Fitch downgraded Russia, bad news about Russia basically becomes a factor for the euro to fall," said Takahide Nagasaki, chief foreign exchange strategist for Daiwa Securities SMBC.
This is because of the euro zone's economic ties with Russia, and also since banks in the euro zone probably have large lending exposure to Russia, Nagasaki said.
Fitch Ratings downgraded Russia's sovereign rating to 'BBB' last Wednesday and said further cuts were possible due to low commodity prices, high capital outflows, melting reserves and corporate debt problems.
Fitch's downgrade followed one from Standard & Poor's in December, making it the second ratings cut for Russia since the end of its last major financial crisis in 1998, when Russia devalued the ruble and defaulted on $40 billion of its debt.