The Times reports a High Court judge will hold the first ‘administrative hearing' of two separate lawsuits on Tuesday. The cases could result in RBS paying out billions of pounds in compensation.
The rights call in dispute came in April 2008, months before the lender took a £45bn state bailout to avoid collapse.
The two cases argue that RBS mis-led investors by failing to disclose the real state of its deteriorating financial position in documentation, therefore breaching the Financial Services and Markets Act 2000.
The report said the first case has been brought by Bird & Bird on behalf of more than 7,000 retail investors, whose total losses are estimated to be about £4bn.
The second case - worth about £360m - mainly deals with institutional investors, including pension funds of miners, local councils and teachers in the UK, US and Canada.
The Times said RBS had declined to comment.