"There is no offer, or any draft of an offer, on the table," a spokeswoman for Carrefour said.
Casino declined to comment.
Casino shares were up 2.7% in early trading in spite of Carrefour's denial. Carrefour shares were down 0.7% at 0725 GMT.
BFM reported that Carrefour had been examining a potential offer for several weeks, citing several unidentified sources.
Initial talk around an all-share bid would value Casino at 4 billion (3.5 billion pounds) to 4.2 billion euros, or a 25% premium to its market value at the end of June, BFM said. That would be equivalent to around 39 euros per share, well below the current share price of 45 euros, analysts at Bernstein said in a note.
Czech businessman Daniel Kretinsky and Slovak partner Patrik Tkac bought a 4.63% stake in Casino last week, leading to a stock rally.
BFM said Carrefour was contemplating adding a cash element to its potential offer, bringing it to the equivalent of 48 euros per share.
Casino has been struggling in a tough business climate in France, where the impact of a price war among supermarket operators has dented retailers' profit margins.
Casino CEO and controlling shareholder Jean-Charles Naouri is hunting for ways to ease the company's debts, and those of parent company Rallye, in part through asset sales.
In May, Rallye was placed under protection from creditors.
Casino's net debt stood at 2.708 billion euros at the end of 2018, and Rallye's stood at 2.899 billion euros.
The two groups were already locked in a dispute amid talk last year of a Carrefour takeover bid for Casino. Casino said in September 2018 that it had rejected a tie-up approach from Carrefour, which Carrefour denied making.
(Reporting by Pascale Denis, Sarah White and Gwenaelle Barzic; Editing by Catherine Evans and Edmund Blair)