Morgan Stanley, JPMorgan and Wachovia are even set to agree terms as early as today.
New York attorney general Andrew Cuomo is currently investigating the apparent presentation of the securities by some banks to clients as being risk-free investments.
He has filed charges against - and subsequently agreed settlements with - Citigroup and UBS over the alleged miss-selling.
The two banks agreed to pay out a combined $250 million in fines and to buy back securities worth $27 billion from the clients.
Under the terms of the new deal with Morgan Stanley, JPMorgan and Wachovia - which now needs to be signed off by state and federal financial regulators - the banks would pay a fine and also pay back clients who bought the auction-rate securities.
The attorney general's office has yet to comment on the report.