Bank BNP Paribas may receive a further €2.5 billion (Dh12bn) in government support, the group's Chairman Michel Pebereau said in a radio interview.
The government recently pledged to invest a further €10.5bn in the country's largest banks to boost lending. France had already injected €10.5bn previously and now said it is willing to put up the same amount.
Under the previous government plan, €2.55bn went to BNP Paribas.
Pebereau said the banks are working with the finance ministry on the conditions, but that BNP would likely be eligible for about the same amount.
The Paris-based bank earlier said it remained "comfortably profitable" in 2008 even after a €710 million ($969m) pretax loss in the first 11 months of the year at its corporate and investment bank.
The company expects 2009 be a "complex" year, BNP Paribas Chairman Michel Pebereau and Chief Executive Officer Baudouin Prot wrote in an advertisement published in French daily newspaper Les Echos.
French lending had climbed eight per cent at end-November from year-earlier levels, they said.
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