Duke's departure isn't imminent, but could be announced in a few months, according to Renee Dudley at Bloomberg News.
The largest U.S. retailer is reportedly interviewing international chief Doug McMillon and U.S. executive Bill Simon, according to Dudley.
Duke had worked at Wal-Mart for years when he took over in 2009. The mega-brand likes to hire executives from within.
McMillon started working at Wal-Mart when he got a summer job there in 1984. Simon joined the brand in 2006.
Both alleged candidates are highly qualified to take the helm.
While McMillon has largely spearheaded the brand's international expansion, Simon is often credited with luring weary U.S. consumers back in stores.
Wal-Mart just reclaimed the top position on the Fortune 500.
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