"London Stock Exchange Group plc announces that it has entered into exclusive discussions with Turquoise Trading Limited, which may lead to a transaction," the LSE said in a brief statement.
"A further announcement will be made in due course," it added without giving any further information.
The takeover talks are the latest attempt by new Chief Executive Xavier Rolet to stamp his mark on the LSE, which is Europe's largest stock market.
Turquoise was launched in September 2008 by nine of the world's biggest investment banks.
The trading platform provides direct competition to leading players like the LSE, pan-European exchange Euronext and Deutsche Boerse.
Arden Partners analyst Sarah Spikes said the LSE would not pay over the odds for Turquoise.
"If the LSE were to buy Turquoise, it would accelerate their pan-European plans -- but I would not expect them to pay much for Turquoise." London Stock Exchange eyes second platform after Sri Lanka firm buy She added that, w