"Such a combination looks potentially interesting as the new entity would become leader in France and Brazil and would be able to benefit from significant synergies," wrote Barclays.
Barclays said it was difficult to ascribe a particular percentage likelihood to this merger happening, but it estimated potential savings at 0.9% of sales of the combined group, or total gross synergies of around 1 billion euros (£903.25 million).
Last year, Carrefour and Casino were locked in a dispute after Casino said it had rejected a tie-up approach from Carrefour, that Carrefour denied making.
Since then, Casino's parent Rallye has filed for protection from creditors.
"We also note that Carrefour CEO has publicly called for consolidation in the sector", Barclays added.
In June, Carrefour CEO Alexandre Bompard said the retail sector was bound to consolidate in the coming years, notably in France as competition intensifies. He added that his mission was to make sure his company emerged as a winner.
Bompard declined to take questions about the possibility of a merger with Casino, when asked about it at a business conference in Aix-en-Provence, southern France, earlier this month.
Barclays has an "equal weight" rating on Carrefour and an "underweight" rating on Casino.
(Reporting by Dominique Vidalon; Editing by Sudip Kar-Gupta)