The shareholders, known as the RBoS Shareholders Action Group, are in talks with litigation funds to launch a formal £3.3bn fund lawsuit against the bank, according to The Times.
The shareholders lost nine-tenths of their money after the bank bought shares in an ill-fated £12bn rights issue.
Shareholders claim they were misled by omissions in the prospectus which concealed the frailty of the bank.
Shares in the rights issue were purchased at an adjusted £20 pounds each, but have now risen to trade at £225.
HSBC, Deutsche Bank and Credit Agricole are three firms backing the shareholder group, The Times reported.