Politicians, including German finance minister Wolfgang Schaeuble have asked private creditors to Greece to accept steeper writedowns on their holdings than the 21 percent losses agreed last July.
Politicians and bankers are still wrangling over how to restructure Greek debt as part of negotiations to reform the common currency.
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EU officials have also demanded that banks prop up their capital cushions to meet a core tier one capital ratio of 9 percent, in a bid to make the financial system more able to withstand a restructuring of Greek debt.
Banks are seen needing just under 100 billion euros with the bulk required by banks in Greece, Spain and Portugal.
Big name banks caught in the crossfire will have to raise less than they feared two weeks ago, and should be able to raise it privately, through existing shareholders or sovereign funds, bankers and analysts said.
To meet the more stringent capital requirements, even large lenders like Deutsche Bank <DBKGn.DE> and Commerzbank <CBKG.DE> are being asked to bulk up their capital position.
Deutsche needs an additional 2 billion euros which it can raise via retained earnings, shedding risk weighted assets, and via a small capital increase if needed, the senior German banking source, who declined to be named, said on Sunday.
The private sector is still striving to reach a deal on Greek debt writedowns by Sunday, another source said.
In July, banks and insurers agreed to contribute 50 billion euros ($69 billion) to reducing Greece's debt via a debt buyback and swap agreement, which equated to a 21 percent writedown. That is now seen as insufficient to make Athens' debt sustainable.
Deutsche Bank <DBKGn.DE> analysts last week outlined a way for banks to contribute a 40 percent "haircut" on Greek sovereign debt without substantially changing the terms of July's debt-relief deal.
(Reporting By Philipp Halstrick, writing by Edward Taylor, editing by Alexander Smith/Ruth Pitchford)