The Food Lion parent has hired Lazard Ltd to sell its Harveys and Sweetbay supermarket businesses, the sources said.
Chief Executive Officer Pierre-Olivier Beckers said the company was looking at options for the units, but declined to comment directly on whether advisors had been appointed to conduct the sale.
"This is a question on the table at the moment," he said on the sidelines of the company's annual shareholders meeting.
Lazard could not be reached immediately for comment.
Delhaize made about 65 percent of its 2012 revenue of 22.7 billion euros ($29.7 billion) in the United States, mainly through its Food Lion and Hannaford chains.
Harveys, which operates 73 supermarkets in Georgia, South Carolina and Florida, focuses on selling regional and fresh products.
Sweetbay, which had 105 stores in Florida at the end of 2012, caters to the Hispanic market.
In January, Delhaize said it would close 34 Sweetbay stores, most of them money-losing.
Beckers, who joined the company as CEO in 1999, announced in early May that he was stepping down.
Delhaize and other traditional grocery chains have come under pressure recently, with discounters like Costco Wholesale Corp and mass retailers like Wal-Mart Stores Inc gaining footing as shoppers' budgets have dwindled.
