The review has been triggered by the departure of APCO director Olly Grender and the arrival of the scheme's new CEO.
FSCS head of communications Heather Tilston said she had drawn up a shortlist of 'fewer than ten' agencies for the account, which she described as a 'mix of PR and public affairs'.
But she added she was interested in talking to other agencies with financial services PR and PA experience for the brief.
Tilston said the review had been motivated partly by Grender's decision to terminate her consultancy relationship with APCO at the end of last month. Grender - who is a former director of comms for the Liberal Democrats and was one of PRWeek's three 'Election Watch 2005' panellists - left APCO to go freelance last year.
She has remained working on behalf of the agency on a freelance basis on the FSCS account but is taking time off to have a baby.
FSCS CEO Loretta Minghella joined last December from the Financial Services Authority.
Tilston said: 'In the past we dealt with a handful of claims mainly involving investment management firms. But we received around 10,000 claims in the last year, many of which were related to mortgage endowment policies and precipice bonds.'
The appointed agency will be expected to boost the scheme's profile among ministers and policy makers. Formal pitches are expected to take place in the next few weeks.