In a statement released by the FSA it said: “Our key priority is to ensure consumers are protected so the FSA Board would need to be convinced that any proposals would be in the interests of consumers.”
The FSA said it has had initial discussions about the proposal and it is prepared to consider the merits of this and other options.
A key consideration for the regulator will be the potential to get compensation to more consumers, more quickly.
It said: “We will continue to hold discussions with the BBA as well as actively seeking the opinions of consumer groups and other stakeholders.”
No changes to existing FSA or future Financial Conduct Authority rules would take place without a full public consultation.
Craig Lowther, managing director of the PPI claims company MoneyBoomerang, said: "The banks' desire to agree an end date to their nightmare is understandable but sympathy is likely to be in short supply.
"We shouldn't forget that the PPI scandal is a mess entirely of the banks' own making."
Lowther said the banks are not settling all the claims currently being made so to impose a limit on the thousands of people who've been let down by their lenders but who have yet to start a claim is unfair.
He said: "The creation of an arbitrary deadline is likely to be counterproductive too as among the surge of new claims triggered there could be a sizeable number of unfounded ones.
"Leaving aside the dubious justification for the deadline even from the banks' point of view it is likely to create more problems than it solves."
And he added: "If one person who was mis-sold PPI loses out on the return of what's rightfully theirs that is one person too many."