Greece has agreed with its international lenders - the European Commission, the International Monetary Fund and the European Central Bank - to sell TT and small lender Proton by mid-July in order to get more bailout funds.

Alpha Bank (>> Alpha Bank S.A.), National (>> National Bank of Greece) and Eurobank submitted binding offers for TT. All three are majority-owned by the Hellenic Financial Stability Fund (HFSF), the bank rescue vehicle that also fully owns TT and Proton.

National Bank Chief Executive Alexandros Tourkolias said, without disclosing further details, the group made an offer for TT. Eurobank also said it bid for the bank.

"We submitted a strong, well-prepared offer for TT to Goldman Sachs, the HFSF's adviser on the sale," an Alpha executive said.

The HFSF hired Rothschild and Goldman Sachs (>> Goldman Sachs Group Inc) as advisers on the sale of Proton and TT.

Authorities wound down TT in January after efforts to sell it failed. They stripped out bad loans from its portfolio and transferred less risky assets and deposits to a new entity called New Hellenic Postbank. The bad loans are being sold.

The HFSF pumped 4 billion euros into the bank to cover a funding gap between assets and liabilities and a further 500 million to recapitalise it.

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 healthy TT has assets of 13.7 billion euros, deposits of 10.7 billion and a network of about 200 branches. Proton is a much smaller bank with deposits of 1 billion euros and 1.3 billion in assets.

(Reporting by George Georgiopoulos; Editing by Steve Orlofsky)