News Group Newspapers is attempting to have the 2006 civil jury verdict set aside at a hearing at the Court of Session in Edinburgh.
Mr Sheridan won the high-profile defamation case over the newspaper after it printed allegations about the then-Socialist MSP’s sex life.
The paper was ordered to pay £200,000 in damages but weeks later a police investigation was launched into allegations of perjury and Mr Sheridan was charged.
He was jailed after being found guilty in December 2010 of lying under oath during the successful defamation action and was freed from prison after serving just over a year of his sentence.
Mr Sheridan, 52, has always denied the allegations and launched an unsuccessful attempt to appeal against his conviction. He has also lodged an application with the Scottish Criminal Cases Review Commission.
The case has returned to the courts as the publisher of the newspaper, which closed down in 2011, now wants three civil appeal court judges to overturn the 2006 decision.
Alastair Duncan QC, representing the newspaper group, has already told the court the verdict should be set aside as it was “unsafe” because of the 2010 perjury conviction.
He also said the verdict could not stand because it was “contrary to the evidence”.
However, during the second day of proceedings yesterday, Mr Sheridan, who is representing himself, said it was his submission that the argument was “irrelevant”.
He told judges Lady Paton, Lord Drummond Young and Lord McGhie: “In any event, the appeal ground on the verdict being contrary to the evidence has no relevance.
“My conviction was not and could not have been evidence led before the jury in 2006.”
Mr Sheridan said he had ten notes of argument to put before the court in his submission, including that some evidence had been “illegally obtained” and was therefore “inadmissible”.
In 2011, the Scottish News of the World closed. Journalists working at the paper’s London office were convicted of phone hacking.
The UK paper’s editor, Andy Coulson, was tried at the High Court in Edinburgh last year for allegedly committing perjury during Sheridan’s criminal trial but was acquitted.
During proceedings, Mr Sheridan used Latin to describe legal processes during submissions but admitted he did not have a strong grasp of the language.
He told the judges: “I apologise for my Latin pronunciation.”
The hearing continues.