Yorkshire and Clydesdale Bank are two of the banks named by the newspaper as set to join the scheme.
Barclays, HSBC, Lloyds Banking Group and Royal Bank of Scotland have already agreed to take part in the scheme.
The scheme pays back consumers who were wrongly sold
interest rate hedging products which protected mainly business bank customers from interest rate movements. Between 2001 to date, around 28,000 of these products were sold to small and medium-sized businesses.

At the launch of the scheme at the end of June, Martin Wheatley, managing director of the FSA Conduct Business Unit, described the scheme as a "difficult and distressing experience" for consumers.
Joseph Eyre, a spokesman for FSA, said more details on the scheme would be released later this week.
He said the scheme aimed to get consumers back to where they would have been had they not invested in the interest rate swap products.
Not all business will be owed redress but those that are could see their original products cancelled or replaced and receive partial or full refunds. These will be assessed by an independent reviewer at each bank appointed by the FSA.