Royal Bank of Scotland said it was in talks to sell its retail investor products and equity derivatives (IP & ED) business, as it slims down its investment bank.
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Several industry sources have identified BNP Paribas, France's biggest bank, as front-runner to buy the business.
RBS, which is 81 percent owned by the British government, declined to say who it was in talks with on Monday. BNP declined to comment.
The British bank said in June it would offload the IP&ED business as it pares down its investment bank to appease lawmakers who want it to focus on lending to domestic households and businesses.
"RBS continues to make progress with its sale of the IP&ED business and is in discussions with a third party in connection with such sale," the bank said on Monday.
The value of the deal has yet to be determined.
RBS has drastically cut the size of its investment bank since receiving a 45.5 billion pound ($73 billion) government bailout in the 2008 financial crisis. Its new chief executive Ross McEwan will publish the findings of a strategic review of the bank next February.
Shares in RBS were up 0.7% at 1023 GMT while shares in BNP Paribas were 0.8 percent higher. The European banking index was up 0.9%.
($1 = 0.6215 British pounds)