The tender, understood to be at RFP stage, covers both corporate and press office work and will involve the incumbent Spider PR, which won the brief from Ketchum in 2011.
A PR source claimed that FedEx, which bought UK courier company ANC in 2006, may be about to face stronger competition in the UK.
Referencing the Government’s sell-off of Royal Mail last autumn for £3.3bn, they said: "There is likely to be a lot of corporate money going in there, which would be a threat for FedEx."
A spokeswoman for FedEx said: "FedEx regularly reviews the relationships it has with external PR agencies and is currently holding such a review with the aim of appointing a UK and Ireland PR agency. At present we are at the initial discussion stage with a number of agencies and are not able to provide any further information at this stage."
FedEx delivers in more than 220 countries and had a global revenue of $11.4bn in the second fiscal quarter ended 30 November.
FedEx Express was recently voted the strongest of transport and logistics brands in the Superbrands survey and 14th in the business category of the survey.