Carlo Tassara, the holding company for French financier Romain Zaleski, has been looking to sell its 26-percent stake in Alior for several years. Poland's banking regulator has given Tassara the permission to seek a buyer by mid-2016.

"There are slim chances that any significant bank will be sold in Poland now due to the Swiss franc rise which has complicated lenders' future. That is apart from Alior, which has no FX loans portfolio. And SocGen is the sole runner now," a source said.

"They are waiting with the whole transaction for Alior to finalise its merger with (small peer) Meritum Bank. SocGen has exclusivity and (the deal) is for sure a matter for the coming months," another source said.

Both Alior and SocGen declined to comment.

The French bank, which already owns small Polish retail lender Eurobank and has corporate operations in Poland, has singled out Poland as a country where it would like to expand its presence through acquisitions.

Sources had said in January that Spain's Santander and Poland's Getin Noble Bank were also in talks to buy the 26-percent stake in a lender which is worth $1.5 billion in total.

(Reporting by Marcin Goclowski and Adrian Krajewski; Additional reporting by Leigh Thomas in Paris; Editing by Keith Weir)

By Marcin Goclowski and Adrian Krajewski