A bankers trade body has appealed to the Financial Services Authority (FSA) to introduce a time limit for customers who were mis-sold payment protection insurance (PPI) to claim back their money.
The British Bankers' Association (BBA) has offered for the banking industry to fund a widespread advertising campaign to ensure consumers are aware of the PPI issue and how to complain as part of the deal.
In response the FSA said in a statement: "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.
"We have had initial discussions and are prepared to consider the merits of this and other options. A key consideration will be the potential to get compensation to more consumers, more quickly we will continue to hold discussions with the BBA as well as actively seeking the opinions of consumer groups and other stakeholders."
The regulator added that no changes to existing FSA, or future Financial Conduct Authority (FCA), rules would take place without a full public consultation.
A spokesman for the BBA said in a statement: "The BBA and its members are committed to improving trust and confidence in banking and we want to ensure that where customers have been mis-sold that they should receive all the compensation that they are entitled to. We will continue to discuss proposals that would achieve these aims with the FSA."
Banks have so far set aside billions of pounds to pay compensation to those who were mis-sold PPI, but appear keen to speed up the compensation payments and draw a line under the incident.
The financial ombudsman has received more than 50,000 complaints about the scandal, which Barclays - the most complained about bank on PPI claims - has set aside £2 billion for.
The Royal Bank of Scotland has put aside £1.7bn, while the Lloyds banking group's bill has reached £5bn.