Plaintiff law firm Maurice Blackburn, backed by listed litigation funder IMF Bentham, said on Wednesday it would investigate a potential class action on behalf of CBA shareholders, citing the hit to the bank's share price.

Maurice Blackburn said it was "astounding" that the bank did not tell investors about the alleged breaches earlier.

The law firm said it could be the largest shareholder class action in Australian history. The current record for a shareholder class action was a $200 million settlement for Centro shareholders of 2012.

CBA noted the potential action, saying it had not been served with legal proceedings but would keep the market informed as needed.

The action is focused on how the bank disclosed allegations that it failed to properly report or monitor suspicious transactions, and that its ATMs were used by criminal gangs to wash millions of dollars.

IMF Bentham said it was investigating claims relating to alleged misleading or deceptive conduct by the bank, and alleged breaches by the bank of its continuous disclosure obligations, relating to Austrac's legal action against the bank.

Each contravention of the Anti-Money Laundering and Counter-Terrorism Financing Act carries a maximum penalty of $18 million, meaning CBA could face a massive fine.

"Austrac alleges that CBA contravened the AML/CTF Act on more than 53,000 occasions. The Austrac allegations are extensive and it is astounding that the market would not be advised of such serious and repeated breaches as soon as the company became aware of them," the national head of class actions at Maurice Blackburn, Andrew Watson, said.

Mr Watson said he was confident the action would proceed, and its size was likely to be "very large" because of the very high number of shareholders in CBA.

Mr Watson pointed to CBA's own statements that it was aware of thousands of alleged breaches of its obligations to report transactions above $10,000 to Austrac in 2015, but had not informed the market.

He also said the bank had made "specific representations" to the market that it was complying with anti-money laundering laws through its website, and documents used in a capital raising and annual reports.

"It's just extraordinary, frankly, that you could have the level of non-compliance which the Austrac pleadings allege, and a board think that that was not sufficiently material that the shareholders should be informed," he said.

The law firm is taking registrations from shareholders who bought the stock between August 17, 2015 and August 3, 2017, the day the Austrac action was announced.

CBA, which has been contacted for comment, has not yet lodged its defence in the Austrac case.

Chief executive Ian Narev has previously said it was alerted to two breaches by Austrac in August 2015, in which it failed to notify authorities of cash deposits above $10,000. Mr Narev said CBA then looked into the matter and found tens of thousands of such breaches, which it said were caused by a "coding error".

The bank has said it did not become aware of Austrac's civil suit against it until it was lodged on August 3.

It has not said when it became aware Austrac was conducting an investigation into the bank, but has maintained it complied with disclosure obligations, which require companies to tell investors about news that is "material".

CBA's share price fell from an intraday high of $84.69 on the day the Austrac action was announced, a Thursday, and opened at $80.11 on the following Monday, Maurice Blackburn said.

"Our investigations and analysis show that this drop was in the top 1 per cent of price movements that CBA experienced in the past five years, making it apparent that the news was of material significance to shareholders," Mr Watson said.

Director of IMF Bentham, Hugh McLernon, said claims from shareholders could be registered from Wednesday.

"CBA is facing most serious allegations from Austrac, and there are serious questions to be answered about what the company knew and when," Mr McLernon said.

The action comes after the corporate watchdog also said this month it was investigating whether CBA and its directors breached the Corporations Act in their handling of Austrac's allegations, including whether it properly disclosed material information.