Tens of thousands of investors have accepted an out-of-court settlement offer from RBS in the case, but a few thousand shareholders remain determined to pursue it, two sources familiar with the talks said.

If they succeed, Goodwin, named in the lawsuit as a defendant, would have to justify his decision-making at the time of the bank's cash call.

The group, which is seeking additional funding of around 7 million pounds ($9.02 million), has also asked for a meeting with RBS's Chief Executive Ross McEwan, sources said.

RBS declined to comment.

Sources said on Wednesday that RBS has been in talks with the last claimant faction over whether the bank would raise its last 82 pence-per-share offer by 20 pence to avert a potentially embarrassing trial that will rake over an uncomfortable chapter in RBS's history.

Judge Robert Hildyard last Wednesday adjourned court proceedings for the third time to June 7 in the case that turns on whether RBS and its former bosses misled shareholders about its financial strength when it launched the rights issue.

Hildyard ordered both sides to notify him of any final out-of-court settlement by Thursday or face trial.

The faction is part of the RBoS Shareholder Action Group, which wrote to its membership on May 27 to say it had accepted RBS's 82p per share settlement offer, valued at around 200 million pounds.

The offer remains a fraction of the 200 to 230 pence per share that shareholders paid for RBS shares in the 2008 fundraising.

The bank was bailed out to the tune of around 45.8 billion pounds just months after its cash call. Shareholders, including thousands of current and former RBS employees, lost around 80 percent of their investments.

RBS, which remains more than 70 percent state-owned, denies any wrongdoing and has said its former bosses did not act illegally.

(Writing by Kirstin Ridley. Editing by Jane Merriman)

By Andrew MacAskill