Two sources with knowledge of the matter told Reuters there had been a meeting on Sept. 12 between Carrefour head Alexandre Bompard and Casino's boss Jean-Charles Naouri to discuss a broad range of topics regarding opportunities for the two.
However, a French government source said the government - which might typically expect to be notified - was not aware of any merger talks between the companies.
France's supermarket groups are looking for ways to bolster profits after a protracted price war at home, and are also under pressure to modernise to counter the moves of online giant Amazon and others into the sector.
Analysts said any merger between Carrefour and Casino was bound to attract close scrutiny by competition regulators, given Carrefour is France's second-largest chain with a 20 percent market share and Casino has nearly 12 percent.
Casino, whose shares have slumped this year due to concerns over its debt, said it had been contacted by Carrefour in recent days over a possible tie-up, adding its board of directors met on Sunday and "unanimously" decided to reject the approach.
"The board of directors also acknowledged the barriers, in France and in Brazil, to a combination with Carrefour, especially in terms of competition and employment," the owner of Monoprix and Geant supermarkets said in a statement.
However, Carrefour - which like Casino has a large business in Brazil - denied making any approach, saying in a statement it was surprised Casino's board of directors could consider "a merger proposal that does not exist."
"The difficulties faced by Casino and its controlling shareholder (do) not justify untimely, misleading and groundless communications," Carrefour said.
(Casino and Carrefour shares this year,
Casino shares fluctuated widely on the contradictory news. They were down 1.9 percent by 0930 GMT, while Carrefour shares were up 0.5 percent.
Carrefour is the world's second-largest retailer by revenues after Walmart Inc, with a market value of about 13 billion euros ($15.3 billion).
Casino, which has been targeted by so-called short-sellers betting on a further decline in its shares as it struggles with its debts, has a market capitalisation of about 4 billion euros.
Ion-Marc Valahu, a fund manager at Geneva-based Clairinvest, which owns some Casino shares, was sceptical about a deal.
"There would be too many regulatory issues, and the two companies have different cultures," he said.
That view was echoed by analysts at investment banks Societe Generale and Bernstein.
"Casino and Carrefour dominate 72 percent of French convenience stores, therefore they would most likely have to dispose of a lot of them. Similarly in Brazil, there would be material disposals," said Bernstein's Bruno Monteyne.
"So the approach from Carrefour to buy Casino seems very unlikely. Combined with the press releases and statements this morning, this seems to be a lot of distracting noise."
The difficulties in clearing major supermarket mergers could also be seen in Britain's decision to probe Sainsbury's takeover of Asda, analysts added.
Casino shares have slumped nearly 30 percent since the start of 2018 as investors fret over its debts and those of parent holding group Rallye. Hedge fund Muddy Waters is one of the firms to have raised concerns over Casino's debts.
Rallye, through which Chief Executive Jean-Charles Naouri controls Casino, needs to repay over 600 million euros worth of bonds in October and 300 million euros worth in March.
Last week, five banks granted Rallye a new 500 million euros credit line, while Casino has also been selling assets to cut debts.
Carrefour shares are down nearly 10 percent this year. In January, it announced plans to cut costs and jobs, boost e-commerce investment and seek a partnership in China to lift profit and revenue.
Roche Brune Asset Management fund manager Meriem Mokdad said the war of words would benefit Casino rather than Carrefour.
"This game of poker is likely to benefit Casino rather than Carrefour as it underlines Casino's underlying attractiveness and value," said Mokdad, whose firm owns Carrefour shares.
(Reporting by Sudip Kar-Gupta; Editing by Richard Lough and Mark Potter)
By Sudip Kar-Gupta and Pascale Denis