The Financial Conduct Authority is considering a deadline for claims over mis-sold payment protection insurance (PPI).
So far more than £20bn has been paid out in compensation for PPI mis-selling to more than 10m consumers.
The regulator will now launch a consultation on whether there should be a deadline on compensation claims.
It said there would be a window of at least two years after the deadline is set.
The FCA cited "increasingly stale" evidence from a high number of customers who are pursuing older cases.
It also said claims management companies are costing customers too much in legal fees.
The number of complaints about PPI is falling, but still runs in to hundreds of thousands every month.
In the first half of 2015 more than 883,000 customers complained about mis-selling, a fall of 16.6% on the same period in 2014.
The FCA said that for now, customers concerned about being mis-sold PPI should continue to bring their claims to the banks involved and to the Financial Ombudsman Service.
The FCA said a deadline would "bring the PPI issue to an orderly conclusion, reducing uncertainty for firms about long-term PPI liabilities and helping rebuild public trust in the retail financial sector."
The regulator said too many people were taking too long to bring their claims, and that a deadline - along with an advertising campaign promoting any potential deadlines - would spur any outstanding claims to be brought.