The loss comes as a blow to Euro RSCG. The account is estimated to have yielded £2 million in income.
The retailer is now holding exclusive talks with CHI, although a formal appointment is not expected for two weeks. DDB London, WCRS and Euro RSCG pitched for the business, while Fallon was ruled out at an earlier stage.
The process was handled through the AAR by the Argos marketing director, Karen Bray. She said: "Euro RSCG has done an excellent job with our current campaign but it is time for us to move on."
The move will bring an end to the "Zac and Pam" campaign starring Richard E Grant and Julia Sawalha, which has run for the past three years.
MindShare, the Argos media agency, is unaffected by the review.