French bank Societe Generale said on Wednesday that it was in discussions to sell its Greek subsidiary Geniki to Greece?s Piraeus Bank.
Shares in Societe Generale, Frances second-largest bank, slid immediately after the announcement and were down 1 percent in late trading.
French banks did a lot of business with Greece and have been cutting their exposure to the country for months.
Earlier this week, competitor Credit Agricole said it was trying to unload its own Greek unit, Emporiki, to Alpha Bank.
Alpha, which is also Greek, said the deal was expected it to be completed by December 31.
Greece is currently struggling to make enough budget cuts to satisfy international creditors who provided the loans that are keeping it afloat day to day. If its creditors refuse to give it its next batch of bailout funds, then the country may have to default on its debts and even leave the euro.