The London Stock Exchange Group said it is looking to sell the French clearing arm of LCH to Euronext NV in a bid to drive through its £21 billion tie-up with Deutsche Borse.
LSE Group said it was exploring the sale of LCH SA to the European exchanges operator as it looks to see off anti-trust concerns raised by the European Commission over the mega-merger.
However, it said there could be no certainty that the talks would lead to a transaction taking place.
The move comes after the LSE Group announced last week that it had received a statement of objections from the European Commission over its proposed merger, but it reflected "a narrower scope of issues".
Following Britain's shock decision to quit the European Union, LSE and Germany's Deutsche Borse have moved quickly to assuage any fears that the referendum result would scupper the deal.
Details of the merger released before the Brexit vote in June, showed that the combined entity aims to make 250 million euro (£210 million) in annual cost savings after five years, in addition to the 450 million euro (£377 million) already flagged, and shed 1,250 jobs.
However, the two exchanges also believe that 550 new roles can be created as a result of the tie-up.