Reports in the weekend press said that Wal-Mart’s chief executive Lee Scott and Carrefour’s chairman, Luc Vandevelde, met in Versailles last month.
The reports said that the executives could have discussed the possibility of Wal-Mart buying a group of Carrefour stores, or a full takeover of the group.
Analysts estimate that any takeover of Carrefour, which operates in 31 countries and is the market leader in nine, would be worth £18bn.
However, industry sources said that if a takeover to took place it would attract the interest of Tesco which is keen to build its international presence.
The French government would also be interested in the deal and could prevent the supermarket group from being taken over. Last month it intervened when rumours surfaced that US soft drinks giant PepsiCo International could be preparing a takeover of French food group Danone. The claims were denied by PepsiCo International.