ATHENS (Reuters) - Geniki Bank, a unit of Greece's second-biggest lender Piraeus Bank, (>> Piraeus Bank SA) has submitted a binding offer to buy New Hellenic Postbank (TT) ahead of a July 15 bidding deadline, Geniki said on Wednesday.

Greece has agreed with its European Union and International Monetary Fund lenders to sell TT and small lender Proton by mid-July in order to get more funds under a 240 billion-euro bailout keeping the country afloat.

Senior bankers told Reuters on Tuesday that three of the country's major banks - Alpha Bank (>> Alpha Bank S.A.), National (>> National Bank of Greece) and Eurobank

All three banks as well as Piraeus are majority-owned by the Hellenic Financial Stability Fund (HFSF), the bank rescue vehicle that also fully owns TT and Proton.

Like other Greek lenders, TT was hit by writedowns on Greek bonds and loan impairments as the country endures its sixth year of deep recession.

The bank was wound down in January after efforts to sell it failed. Bad loans were stripped from its portfolio and the less risky assets and deposits were transferred to a new entity called New Hellenic Postbank. The bad loans are being sold.

(Reporting by Karolina Tagaris; editing by Tom Pfeiffer)