France's largest banks are stepping up moves to unload their Greek subsidiaries and sever their unhappy ties to the crisis-hit country -- whose future in the euro zone is still shaky.

Societe Generale SA (EPA: GLE), France's second-largest bank, said Wednesday it is in talks to sell its 99.1 percent stake in its ailing Greek unit Geniki Bank to Piraeus Bank SA.

"Although these discussions are at an advanced stage, no decision has yet been made by either party," Societe Generale said in a statement.

The disclosure from the French bank came just a day after Credit Agricole SA (EPA: ACA), France's third-largest bank, said it expected to sign a deal to sell its troubled Greek arm, Emporiki Bank, to another Greek bank "in a matter of weeks."

The French banks once had grand ambitions in Greece and other Southern European countries when times were good. They bought their Greek bank interests in the past decade, hoping to gain entry into a promising new region.

Back then, Greece's economy was growing at twice the rate of the rest of Europe. However, when Greece's finances deteriorated and helped trigger the European debt crisis three years ago, Societe Generale and Credit Agricole wound up being among the most exposed of any European banks to Greece.

Their earnings have been badly bruised by their ill-fated expansion binge.

Credit Agricole reported Tuesday €370 million in losses in their holdings of Greek government bonds, due to the country's debt swap earlier this year. These losses were one of the biggest causes of a 67 percent slide in Credit Agricole's second-quarter net profits.

Emporiki has been a drag on Credit Agricole's earnings almost since the French bank acquired it in 2006.

Late last month, Crédit Agricole injected €2.3 billion ($2.9 billion) of capital into Emporiki, which may not prove enough to pave the way for a sale, the Wall Street Journal reports, citing an anonymous source. Crédit Agricole may be asked to again recapitalize its Greek unit before it is sold to avoid forcing Greece to pump taxpayers' money into the ailing lender, the person said.

Societe Generale has been in a similar position. The French bank bought Geniki in 2004 and has been losing money for the last several years, with losses of €796 million in 2011 and €411 million in 2010.

Earlier this month, Societe Generale posted a 42 percent drop in its second-quarter profit and missed analysts' estimates.

Fears that Greece could exit the euro zone had also raised uncertainty for the banks, leading them to follow in the footsteps of other large international companies like Carrefour SA (EPA: CA), the big French supermarket chain that two months ago sold off all of its Greek operations.

Shares of Societe Generale SA (EPA: GLE) fell 1.85 percent to close at €20.47 in Paris trading. Credit Agricole SA (EPA: ACA) shares closed up 0.37 percent at €4.31 apiece.