The Texan believes he was the victim of an “epic swindle” when the club was sold against his wishes to New England Sports Ventures for £300 million (€352m).
The sale went ahead after Mr Justice Floyd granted anti-suit orders which prevented Hicks taking action in the Texas courts.
If Hicks is successful at the new two-day hearing, he will be able to make damages claims against the Royal Bank of Scotland and former club directors.
Paul Girolami QC, representing Hicks, told the same judge yesterday that he was applying to strike out or dismiss claims by Martin Broughton, former chairman of the club, seeking damages against his client for his actions while owner.
He said he also sought to discharge the anti-suit injunctions which were granted to stop any frustration or obstruction of action being taken in the British courts over the sale.
Actions brought by RBS against Hicks are no longer in issue and should be stayed, he said.
The bitter courtroom battle began last October and ended with the sale of the club.
Now Hicks is seeking to clear the way for a series of multi-million-pound damages claims against the bank and former club directors.
RBS wants to block Hicks and his former partner George Gillett from suing over the sale in which they lost £140million (€164m).
New England Sports Ventures is also applying to the court to be added to the application for a permanent anti-suit order blocking legal action outside Britain and the EU.
It bought the club after repaying a £237million (€278m) loan Hicks and Gillett took out with RBS and Wells Fargo and Co.