Investors have until 26 October to express their interest in the Ljubljana-based state-owned bank.
Once SSH establishes what interest there is to buy the bank, qualified investors will be invited to submit non-binding bids, according to a posting on SSH's website.
SSH had named French bank BNP Paribas the sole financial advisor carrying out the procedure of selecting the best bidder.
The holding reserves the right to change or stop the procedure any time, and says it intends to maximise the proceeds from the sale.
Since a qualifying stake is being sold, the buyer will have to get clearance from the European Central Bank.
The management of Abanka did not want to comment on the news. It said that the bank was doing well, its stability and capital adequacy confirmed by the international ratings agency Fitch Ratings.
Asked to comment on the announcement, Former Finance Minister Dušan Mramor said it was hard to tell whether the stake of Abanka to a strategic partner would yield better proceeds than an initial public offering (IPO), like in the case of the NLB sale.
The economist told the press on the sidelines of an event in Portorož that the interest on the market from strategic institutional investors and from investment funds which want to invest their surpluses should be checked.
Mramor added that the current interest of financial investors in minority stakes was relatively high, while interest of potential strategic investors who would like to enter Slovenia or strengthen their position in the country was not as clear.
Matej Šimnic of asset management firm Alta Invest told the STA that the bank's price would depend on the interest and reserves recognised by potential buyers during due diligence.
He believes that the players already present on the Slovenian banking market are ready to offer a good price, but he added that "it is true that we did not see that in the case of Gorenjska Banka."
Lojze Kozole of the brokerage Ilirika meanwhile said that the price "could most probably stand between 0.6 and 0.8 of the book value," adding that a large bank which wanted to expand in Slovenia or a private equity fund could respond to the invitation.
The book value of an Abanka share, according to the latest data on the bank's website, was EU 38.34 at the end of 2017. This would put the potential sale price of the bank estimated by Kozole at between EUR 347m and EUR 463m.
The state has been Abanka's sole owner since a massive bank bailout in December 2013 which also saw the state salvaging NLB, NKBM and Banka Celje.
In exchange for the European Commission's approval of the state aid, the government had to commit to sell Abanka by the middle of 2019.
The bank reported EUR 40.4m in net profit in the first half of the year, up 24.5% from the same period last year.
Its total assets amounted to EUR 3.7bn at the end of June, up 1.4% from the end of 2017, putting its market share at 9.6%.
This year it will pay EUR 42.6m in dividends into the state budget.
The bank, led by Jože Lenič, was set up in 1955 as a subsidiary of the Yugoslav Bank for Foreign Trade as the first bank for international trade in Slovenia.
It transformed into Abanka in late 1989, merged with Banka Vipa in 2002 and then as part of the bailout with Banka Celje in October 2015.
