Reuters reported in June that SocGen was exploring a sale of Eurobank, given increasing competitive pressures on the business.

Sources said at that time Santander, Credit Agricole

"Millennium, Credit Agricole are in the game and Alior has joined too. Santander's BZ WBK is not in the transaction. For Alior this is a continuation of a strategy to develop through takeovers," a source familiar with the transaction said.

Two other market sources also said Millennium had submitted an offer and one of them confirmed that Alior Bank had recently joined the process.

Puls Biznesu daily quoted unnamed sources saying Millennium and Alior had submitted their offers to buy Eurobank.

Millennium Bank and BZ WBK declined to comment.

Alior said it would not comment on the deal, but said in an emailed statement:

"The market is consolidating, and Alior Bank wants to be an active participant in this process. We have significant experience in effectively conducting such transactions. Eurobank is an interesting takeover subject, with a well-ordered business."

Later, in a separate statement, Alior said "it focuses now on organic growth and on the execution of its 'Digital Rebel' strategy."

Alior Bank has a market capitalisation of 8.8 billion zlotys (1.8 billion pounds) and is the ninth biggest bank in Poland by assets. PZU, state-run insurer, has a 32 percent share in the lender.

As Alior is a state-run entity the potential deal would fit into Poland's strategy to buy back assets from foreign investors such as banks, shipyard, and energy assets. On Wednesday state run fund PFR announced it will buy a 35 pct stake in a Polish bus producer Solaris from Spanish firm CAF.

Poland's government, which is run by the nationalist Law and Justice (PiS) party, says that the European Union's largest former communist country is too dependant on foreign investors, who bought into Polish assets in the 1990s and 2000s.

Eurobank is the 17th largest Polish bank with assets of 14billion zlotys. Last year, it made a net profit of 103 million zlotys.

The sale of Eurobank would reinforce a broader trend of consolidation in Poland's banking sector, which has accelerated in the past few years.

(Reporting by Agnieszka Barteczko, Anna Koper and Marcin Goclowski; editing by David Evans)