* Alpha, Attica, Eurobank, and National Bank make offers
* Bank support fund HFSF to assess offers
* Postbank being split into good and bad parts (Adds banks confirming interest)
By George Georgiopoulos
ATHENS, Jan 4 (Reuters) - Four Greek banks have made offers for state-controlled Hellenic Postbank, a senior banker close to the process said, in the latest step in the battered sector's consolidation.
Postbank, 44 percent government-owned and deemed to be not viable, is being divided into two parts - a "good" business that will be sold or run as a stand-alone entity, and a "bad" bank that will be liquidated.
Alpha Bank, Attica Bank, Eurobank and National Bank have all made non-binding offers for Postbank, the banker told Reuters on Friday. He asked not to be named.
Later in the evening, all four banks issued statements confirming their interest in Postbank but without disclosing whether they had submitted offers.
"Alpha Bank confirms its initial interest in the TT Hellenic Postbank," it said in a statement.
The other three banks declined to issue further comment.
Battered by rising bad debts and losses from government bond writedowns, Greek banks have been consolidating to help cope with the fallout from the country's devastating debt crisis.
To that end, Eurobank is considering an offer from National Bank to form the country's largest bank group. Eurobank and National Bank each own stakes of about 5 percent in Postbank.
Postbank itself holds a 22 percent stake in smaller Attica Bank, which analysts have said was a likely suitor.
While the Bank of Greece, the central bank, is running the process to sort out Postbank, initial offers will need to be cleared by the Hellenic Financial Stability Fund.
Set up as a capital backstop for viable banks, the HFSF has a say on Postbank because it will be the major shareholder in the top four lenders when their recapitalisation is completed this year.
"Banks that have received support by the HFSF must submit their interest to the fund for approval before binding bids are routed to the Bank of Greece," an HFSF official told Reuters.
After HFSF grants approval, binding offers can be submitted to the central bank.
Greece and its international lenders have earmarked 50 billion euros ($65 billion) from the country's 130 billion bailout to recapitalise four systemically important banks and wind down others deemed not viable.
The big four - Alpha Bank, Eurobank, National Bank and Piraeus - have already received support from the HFSF.
They got an 18 billion euro advance in May and another 9.5 billion in December, for a total to 27.5 billion - the amount the central bank had said was needed to restore their solvency ratios.
Under the plan, the four will have to issue new shares to achieve a core tier 1 capital solvency ratio of at least 6 percent and contingent convertible bonds, or CoCos, to boost the ratio to 9 percent.
The timetable for their recapitalisation calls for completion of CoCo issues by the end of January. The contingent convertible bonds will be underwritten by the HFSF.
Banks' share issues must be completed by the end of April.
The Greek bank stock index closed up 5.5 percent. (Editing by Dan Lalor and Mike Nesbit)