Cypriot banks will receive the bulk of the 10 billion euros $13 billion (8.6 billion pounds) that Nicosia will get from euro zone countries to stave off bankruptcy. Unlike in previous bailouts for other nations, the rescue package is co-funded by levies on bank deposits.

Units of Cypriot banks in Greece, which account for about a tenth of the country's banking market, were specifically excluded from the levy after a deal to transfer them to other lenders.

"The Bank of Greece will explore the interest of Greek banks in purchasing these assets," Finance Minister Yannis Stournaras said after a conference with the country's central bank Governor George Provopoulos.

Cyprus's two top lenders with a presence in Greece are Bank of Cyprus and Popular Bank. Greek operations accounted for more than a quarter of total group operating income at Bank of Cyprus and 10 percent at Popular, according to nine-month 2012 results.

The interest will be explored as quickly as possible, perhaps even before Tuesday when Greek lenders open again after a Monday holiday, a senior central bank official told reporters on condition of anonymity.

Greek lenders have themselves been bailed out with up to 50 billion euros in EU/IMF funds after a government debt restructuring in 2012 severely hit the value of their bond holdings.

A likely buyer was Hellenic Postbank, a formerly state-controlled lender which was itself bailed out in January, three banking sources told Reuters.

Postbank, whose capital shortfall was estimated at 3.7 billion euros, passed into the full ownership of Greece's bank bailout fund (HFSF) with a view to being sold at some point to private investors.

"It seems that the Postbank is seriously considered," one senior Postbank manager said.

Euro zone finance ministers said earlier on Saturday after the Cyprus bailout they welcomed the prospect "that an agreement could be reached on the Greek branches of the Cypriot banks, which protects the stability of both the Greek and the Cypriot banking systems".

Cypriot units' takeover would be done in a way which would not burden Greek debt, Stournaras said.

(Reporting by Harry Papachristou; Editing by Jason Webb)