The morning meeting between Carrefour head Alexandre Bompard and Casino's boss Jean-Charles Naouri took place at an unidentified third party location, the sources added.
One of the sources said the discussions were about a "more general reflection regarding Casino's assets."
Separately, a French government source said the French government was not aware of any merger talks between Casino and Carrefour.
Major deals involving France's biggest companies typically require input from the French government to see if the government would allow it, given the risks to jobs and the impact on French consumers.
Casino said late on Sunday it had been approached by Carrefour about a tie-up. Carrefour denied any such approach.
(Reporting by Pascale Denis and Yann Le Guernigou; Editing by Luke Baker/Sudip Kar-Gupta)