In a statement, the market regulator said now is the time for banks and other financial institutions to consider their contingency arrangements and what steps they may need to take to address possible issues.
The organization added that it has already started contacting "high impact" firms including infrastructure providers to determine whether the flu outbreak is affecting any aspect of their business.
In 2006, the FSA ran a market-wide exercise examining the likely impact of a flu pandemic on the British financial services sector.
The exercise found that in such a scenario, absenteeism within the industry would probably peak at 49 per cent, with some business units experiencing absenteeism "clusters" of up to 60 per cent.
It called for more work on strategies to ensure that cash distribution is maintained and branch closures are better coordinated.