Talks between the London Stock Exchange (LSE) and the heads of two European bourses are set to resume next week.
The rival suitors are set to put their cases to the LSE
The heads of LSE's suitors Deutsche Boerse and Euronext both met LSE head Clara Furse last week, a source close to the negotiations told BBC News.
The two bourses are locked in a bid battle and further talks to explain the benefits of both bids have been scheduled for the new year.
A £1.3bn ($2.5bn) offer from Deutsche Boerse has been rejected by the LSE.
In a 13 December statement, the LSE said the proposal undervalued its business but agreed to hold talks with Deutsche Boerse to ascertain whether a "significantly improved proposal" would be in the interests of LSE's shareholders and customers.
Paris-based Euronext, which owns the Liffe derivatives exchange in London and combines the Paris, Amsterdam and Lisbon stock exchanges, has also begun talks with the LSE.
The meetings in January with the German bourse's chief Werner Seifert and his rival bidder Jean-Francois Theodore
are set to build on discussions held on 21 December in London.
Deutsche Boerse has held a total of two "very constructive" meetings with the LSE since its initial proposal was made, a spokesman said.
Further talks between Mr Seifert and Ms Furse are expected to focus on the benefits of putting the London and German markets on one technological platform.
Deutsche Boerse has long wanted to link up with London. The two tried and failed to seal a merger in 2000.
Commentators have said that a deal with Euronext could potentially offer the LSE more cost savings than a deal with Deutsche Boerse.
But a deal with either bidder should, theoretically, make it easier for shareholders to invest in overseas companies and markets.
It would also create the biggest stock market operator in Europe and the second biggest in the world after the New York Stock Exchange.