Talks are at an informal stage, but it is thought that American Express plans to draw up a pitchlist for the account later this year.
It is not known whether OgilvyInteractive, the incumbent, will repitch.
Most of American Express' advertising and media business is held by Ogilvy and MindShare, both owned by WPP, but the US-based company uses a roster of agencies to handle its global online advertising and media projects.
Last year, the credit card company handed Greenlight a UK brief to handle its search marketing after a three-way pitch against Media Contacts and The Search Works.
The digital agency TBG handles American Express' online media planning and buying in the UK as well as some direct response work.