* Offer priced at 2-2.6 euros a share - sources
* Demand for more than 2.5 bln euros of new shares-source
* Bookbuilding to close on Thursday (Recasts, adds details of offer, background)
By George Georgiopoulos and Freya Berry
ATHENS/LONDON, May 7 The National Bank of Greece (NBG) has set the price range for a share placement worth up to 2.5 billion euros ($3.5 billion), which bankers said was the latest deal by a Greek lender to see strong demand from investors.
The NBG is seeking to shore up its balance sheet and is the fourth Greek bank in the past six weeks to see strong demand for a share sale, as investors hunt for bargains amid a nascent economic recovery in the bailed out country.
Two sources familiar with the matter said on Wednesday that the NBG placement had been priced at 2-2.6 euros a share, in a deal worth up to 2.5 billion euros.
One of the sources added the books had already been covered by Tuesday night, the day the bookbuilding process was launched, and that demand had been strong.
"We did see some very big orders coming through," the source said.
A banker told Reuters earlier on Wednesday the placement was oversubscribed "by more than one time so far".
Yield-hungry investors have snapped up recent offerings from Greek peers Alpha Bank, Piraeus and Eurobank .
Those three lenders have raised 5.81 billion euros between them through similar equity offerings over the past six weeks, as investor confidence in the recession-battered country improves. Piraeus saw over 3 billion euros of orders for its 1.75 billion-euro placement in March.
NBG, the country's largest bank by assets, is tapping international markets to plug a 2.18 billion-euro capital hole revealed in a central bank stress test in March.
Banks are busy shoring up their balance sheets in a bid to boost their capital position ahead of the European Central Bank's November health check, when it becomes their supervisor.
NBG's existing shares were trading 3.2 percent lower at 2.72 euros on the Athens bourse at 1421 GMT.
Bookbuilding will end on Thursday, with Goldman Sachs and Morgan Stanley acting as global coordinators and bookrunners, joined by BofA Merrill Lynch, Citigroup, HSBC, UBS and Mediobanca.
NBG has a current market value of 6.73 billion euros and is 84 percent-owned by Greece's bank bailout fund, the Hellenic Financial Stability Fund (HFSF).
Proceeds from the sale will be used to cover the difference between the identified capital hole in the health check, and planned moves to boost capital by 1.04 billion euros that have been approved by the Bank of Greece.
NBG also plans to buy back 1.35 billion euros of preferred shares from the government. Its equity offering does not include pre-emption rights for existing shareholders, including the HFSF.
($1 = 0.7177 euros) (Editing by Harry Papachristou, Greg Mahlich and Mark Potter)