The FSA is inviting comments by August 29.
The watchdog is considering telling customers about the banks with the highest number of complaints, and showing how well they dealt with them.
Steve Brooker, senior policy advocate of the National Consumer Council consumer group, said: “The proposal will encourage the industry to improve the way it deals with customers. “Companies will be encouraged to compete on quality and not just price.”
Peter Tyler, a policy director at the British Bankers’ Association, said it would be extremely difficult to put the information in the correct context and make it useful for consumers considering whether to switch banks.
He said the proposal would also go against the FSA’s own intention not to name and shame banks.