Brunswick has done financial comms for Bupa for the past ten years and is repitching for the work.
The global account also involves raising the profile of Bupa CEO Stuart Fletcher, and the company's spokespeople.
The brief can be split in two, in which case two agencies will be appointed, or a single agency will carry out the entire brief.
The process is being managed by Bupa head of comms, Jo Hudson.
A Bupa spokesperson said: "We regularly review our agency relationships across Bupa. This brief is for our global reputation building and financial communications activities and does not affect any of the agencies working with our UK businesses."
The review follows the arrival of corporate affairs director Alex Cole, who joined Bupa last year from Sainsbury's.