Mindshare is the incumbent on the business, while M4C handles media buying.
The body, which launched in 2000 to help savers who have lost money invested with banks, has approached selected agencies inviting them to pitch for the business.
It wants an agency to plan the second phase of an awareness campaign launched in the first quarter of last year.
The FSCS stated in its brief that it is looking for an agency that has experience of engaging audiences with a "low-interest subject matter". Agencies must respond by 10 February.
Michelle Rajendran, the FSCS marketing manager, is leading the process.
The FSCS last held a pitch for its communications planning in 2009. McCann Manchester, which is responsible for the creative business, is not affected by the review.