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* Banks and advisors pushing for change
* Banks want deal that would see more private investment, sooner
* HFSF sees some merits but focused on Eurobank's 2 bln-euro capital hike
* Any change likely to be scrutinised by EU/IMF
ATHENS/LONDON, Nov 25 (Reuters) - Some of Greece's biggest banks and their advisors are starting to press the country's banking rescue fund to look at ways to speed up their return to wider private ownership, banking sources say.
Armed with 50 billion euros ($68 billion) from the country's 240 billion-euro EU/IMF bailout, the Hellenic Financial Stability Fund (HFSF) was set up to recapitalise the top four banks and cover the cost of winding down others deemed non-viable,
The HFSF duly took majority stakes in these four banks in the summer with the injection of new equity capital and, with the exception of Eurobank, private investors agreed to buy at least 10 percent of the new equity and got the option to eventually buy out the HFSF with the issue of warrants on all of its shares.
However, Piraeus Alpha Bank and National Bank of Greece now face being stuck with over 80 percent ownership by the HFSF until the warrants, which currently trade at a premium, reach their final exercise dates in late 2017 for Alpha and National Bank and January 2018 for Piraeus.
Strike prices vary by institution but typically warrant holders in Alpha can buy shares from HFSF at 0.4488 euros on Dec. 10, 2013 or at 0.4567 euros on June 10, 2014, while shares in free float were trading around 0.6520 euros on Monday, a rise of 30 percent in the last three months.
Meanwhile Eurobank, which was rescued by the HFSF alone after it failed to attract private investors, now aims to raise 2 billion euros in a new share sale, diluting the HFSF's warrant-free stake of 95.2 percent in a first step towards privatisation.
With Greece's economy on the cusp of returning to growth in 2014 after six straight years of recession that shrank national output by a quarter, investors' interest in the often-embattled country is on the rise.
The Athens banking sector index for the five banks that are traded is up 29 percent since early July and last month U.S. hedge fund investor John Paulson, who has investments in Alpha and Piraeus, said the sector remains an attractive investment play on the country's recovery.
For now the HFSF is focused on getting private investors into Eurobank with the 2 billion-euro share offer, a process which might not be completed until March 2014.
But a senior banker in Athens said that his institution and others have still been in discussion with the Greek financial authorities about ways to change the warrant structure at their banks and that the ideas were being well received.
"They 1/8the authorities 3/8 recognise that there are arguments to support the early retirement of the warrants," he said, adding that the proposals would be favourable for the HFSF because it would no longer face a 'cliff' of all the warrants being exercised together.
However, any changes would have to be approved by the troika of European Commission, European Central Bank and IMF officials overseeing Greek's bailout, who would be keen to make sure any changes did not disadvantage the HFSF or gift overly generous terms to the private investors.
A banker familiar with the HFSF's position said the proposals had mainly come from investment banks.
"This proposal came out of the blue, we are not sure it can be done under the current framework," he said, referring to the deal agreed when the banks were recapitalised.
"The idea is that the HFSF could tender to buy back the outstanding warrants, offering their holders stock, cash or new warrants which could have a longer maturity, or lower strike price," he said.
"There are a multitude of structures that could be considered on new warrants, but this is still in the sphere of ideas. It is not our focus right now."
For now, the holders of the warrants, which have a market value of about 2 billion euros, according to the person familiar with the HFSF's position, are not holding out much hope.
"It's clear that all discussions which are currently aired are purely speculative given Eurobank's capital increase will only take place early Q1 (2014)," said Achilles Risvas, chief executive of Dromeus Capital, a hedge fund which holds Greek warrants.
"Anything that would unlock or help realise future upside for current holders of the warrants would be worth considering."
The HFSF declined to comment, while spokesmen at Piraeus, NBG, and Alpha were not immediately available to comment. ($1=0.7394 euros)
(Editing by Greg Mahlich)