The operator of the rail link between London and continental Europe hired AMV as its pan-European ad agency in February 2012 after a competitive pitch.
AMV beat CHI & Partners (working with JWT Paris) and Leg (partnering Havas Worldwide London) to the business.
The incumbent in the UK was Fallon, which had dropped out of the process at an earlier stage.
AMV’s "stories are waiting" campaign for the brand picked up a bronze Film Lion at Cannes last month.
A spokesman for Eurostar said: "We would never comment on the details of any conversations we may or may not have with suppliers at any time. Our relationship with AMV is ongoing."