The two countries are under pressure to reach an accord ahead of a meeting on Sunday of the bank's board of directors.
The Belgian and French prime ministers, Yves Leterme and Francois Fillon, held telephone talks on Saturday morning, said a source, followed by afternoon discussions between finance ministers Didier Reynders and Francois Baroin.
And according to one official in Belgium, Leterme and Fillon -- as well as officials from Luxembourg -- would meet in Brussels on Sunday to discuss the issue further.
The two governments "are discussing the price of Dexia Bank Belgium" --the bank's Belgian arm which the Belgian state now wants to buy, added Elke Maes of the LBC-NVK labour union which represents Dexia employees.
"We hear that it is not easy," she told AFP.
A government source said a meeting of cabinet ministers was expected to be held in Brussels later Saturday, but it was not yet known whether there would be an announcement on the future of Dexia.
Belgian media reported that the two countries, both Dexia shareholders after a 2008 bailout, are seeking agreement on the sale price of Dexia shares, including in its Belgian retail banking arm.
They also need to agree on the guarantees needed to back up a so-called "bad bank" that will remain after Dexia's dismantling to hold high-risk assets.
The first stumbling block was the price for Dexia Bank Belgium.
Belgium is seeking to pay the lowest possible price, a problem for French shareholders who want a lucrative deal and favour a transfer to another bank, said the Belgian economic daily l'Echo.
It estimated the price for the bank between 3 billion and 7.5 billion euros ($4 billion to $10 billion).
Several banks, including Deutsche Bank, Rabobank, Credit Mutuel and BBVA, have shown interest in Dexia Bank Belgium, said the Belgian press.
Another sticking point: what share each government will cover in guarantees for the bad bank's portfolio.
France favours a division of 60/40 or even 65/35 with Belgium taking the bigger bite, said l'Echo. Paris fears that taking a bigger share may see it lose the top AAA credit rating that allows it to borrow cheaply on the international financial markets.
Credit ratings agency Moody's warned Friday that Belgium could be downgraded over its support for Dexia.