The sale of the NBGI business is part of a strategy to divest non-core assets as Greece's largest lender implements a restructuring plan to bolster its balance sheet.

"We are now going through the second round of the secondary sale process. We believe that this is an imminent thing," Christodoulou said in an interview. "It’s most likely that it will be done by end-September."

NBG is one of Greece's top four banks that were bailed out by the European Union and International Monetary Fund, which set aside up to 50 billion euros ($68 billion) in a rescue fund to clean up the sector after its battering in the country's sovereign debt crisis.

Christodoulou would not specify how many bidders were left, but said it was about a quarter of those that had initially shown interest. The business manages about 900 million euros in assets and has been on the market since January.

He said the transaction would not have a material impact on the NBG's capital ratios.

The deputy CEO said NBG may issue more debt soon to follow a 750 million euro ($1 billion) five-year bond issued in April at a lower interest rate than the Greek sovereign.

"If we find there is a market, there is a format, that is not competing with the issue we place, we could be in the market much sooner (than the next few months)," he said.

Greece's top four lenders - NBG, Piraeus, Eurobank and Alpha - have all returned to capital markets with equity and bond issues as international investors warm to the country's economic recovery prospects.

"We are happy to see the investors sit on some good performance and feel good about it as opposed to putting pressure on the market," Christodoulou said.

NBG, which delivered better-than-expected profit in the first quarter, helped by lower funding costs and its Turkish unit Finansbank, will be among the group of euro zone big banks facing a European Central Bank (ECB) health check later this year.

"Given that we have just finished the stress tests for the Bank of Greece as recently as last March, we believe that it’s very recent and fresh, as contemporary as it gets," said Christodoulou, signalling optimism over the ECB checks.

Paul Mylonas, NBG's general manager for strategy and research, said the bank would not be able to use the ECB's new 400-billion-euro programme of cheap funding to increase lending.

The programme, dubbed the TLTRO, was unveiled on June 5 and allows banks to borrow money for four years at a fixed low cost so they can lend more.

"The problem of the Greek banks is the lack of collateral eligible to the ECB, we cannot increase our exposure to the ECB but what we can do is replace the short-term exposures that we have with longer term," said Mylonas.

Banks can only borrow from the ECB if they have collateral, such as bonds or other assets, to secure the debt against.

"Other European banks will have the opportunity to borrow more and for there to be more liquidity; it could have a secondary impact which could be important for Greece," said Mylonas. "Directly we will not see anything."

($1 = 0.7357 euros)

(Writing by George Georgiopoulos,; Editing by Jason Neely and Mark Potter)

By Laura Noonan and George Georgiopoulos