The ECB's decision-making body meets on Thursday and cash-strapped Greek lenders, which have been relying on expensive ECB emergency funding, had been hoping it would decide to resume accepting Greek government debt as collateral.

That would give Greek banks access to the ECB's weekly auctions, where banks can borrow at a zero interest rate.

But Greece has a 'junk' credit rating, so the condition for reintroducing such a 'waiver' on Greek government debt is that the country is deemed compliant with its rescue programme.

Hopes of this happening had been growing since last week's agreement between Alexis Tsipras' government and its lenders on the bulk of reforms.

But the leftist government is resisting some of the additional measures asked of it, such as phasing out a top-up benefit to pensioners. That makes approval by the ECB on June 2 unlikely, the sources said.

They cautioned the matter was still uncertain and the final decision would only be made by the ECB's Governing Council when it met in Vienna on June 2.

One source added the waiver may be reinstated only after euro zone governments give the all-clear to Greece. Euro zone deputy finance ministers are expected to meet again next week to prepare for a Eurogroup meeting later in the month, where decisions can be made.

The ECB declined to comment.

Greek banks lost access to the ECB's weekly auctions last year when Athens refused to meet its bailout commitments, exacerbating its debt crisis and almost pushing the country out of the euro zone.

Since then, banks have relied on the ECB's Emergency Liquidity Assistance, where the average interest rate charged is estimated to be around 100 to 150 basis points above the ECB's benchmark rate.

Reinstating the waiver would also be a first step towards making Greek debt eligible for the ECB's bond-buying programme, provided that Athens passes a debt sustainability review by the ECB.

(Editing by Larry King)

By Balazs Koranyi and Francesco Canepa

Stocks treated in this article : Piraeus Bank SA, National Bank of Greece, Attica Bank SA