According to Bloomberg, two people familiar with the matter claimed Bank of America and JP Morgan Chase, as well as three other mortgage servicers, made the proposal during settlement talks in Washington.
The moves came after state attorneys general and federal officials offered a chance for institutions to finance principal writedowns for homeowners.
Claims of faulty foreclosure practices were triggered after the housing collapse.
Banks and Republican attorneys general voiced opposition to the original settlement proposal as they feared the action would serve to reduce principal amounts for borrowers.
Recent rankings compiled by Bloomberg placed just three US lenders in its top 20 list of the strongest banks in the world.
Fifth Third Bancorp came in seventh position, JP Morgan Chase ranked in 14th and Citigroup was placed in 16th spot.
By Asim Shah