The company, one of the biggest banks in the US, has called the review as it attempts to merge its own credit-card offering with Egg and build on the latter's existing presence in Europe.
The winning agency will be briefed with creating online advertising to back a number of new product launches, as well as brand-building work to increase its presence on the continent.
The work will also include some back-end site build and infrastructure development as the company looks to improve its customer experience and ease of use.
It is thought that once the merger is complete and the digital campaign is underway, the company will then invest in a pan-European above-the-line campaign to promote the change across traditional channels.
The work will be created by Publicis, which picked up the £300 million global Citibank advertising account last April.
Egg hit the headlines this week when it decided to withdraw its credit cards from 161,000 customers whose credit profiles, it claimed, had deteriorated. But reports suggested the move was part of an attempt to offload low- risk, low-profit customers.