The bid follows a June 13 offer by Credit Agricole to buy 100 percent of Emporiki, valuing the Greek bank for US$3.9 billion at US$29.69 per share.
Agricole has a six-year partnership with Emporiki and already owns 8.9 percent of the bank, in which the Greek state controls about 41 percent.
Acricole Chief Financial Officer Gilles de Margerie has said the French bank would not raise its bid if another suitor emerge and would consider selling its holding if there is another bid. Agricole couldn't immediately be reached for comment.
Greek Finance Minister Giorgos Alogoskoufis, who met senior Bank of Cyprus officials in Athens on Wednesday, has invited potential investors willing to match Credit Agricole's offer to submit their bids by the end of July, according to the AP.