American Express Co
American Express shares fell about 3 percent to $83.65 in premarket trade.
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Costco has already replaced American Express with Capital One Financial Corp
"We were unable to reach terms that would have made economic sense for our company and shareholders," American Express CEO Kenneth Chenault said in a statement.
The current agreement is set to end on March 31, 2016, American Express said.
Costco has 468 warehouses in the United States and Puerto Rico, and caters to relatively higher-income customers than Wal-Mart Stores Inc
(Reporting by Avik Das in Bengaluru; Editing by Savio D'Souza and Sriraj Kalluvila)