Glenn Mulcaire is appealing against a court ruling that he cannot rely on privilege against self-incrimination, meaning he does not have the power to refuse to answer questions put in civil cases.
Currently, Mulcaire would have to reveal who asked him to provide details of voicemail numbers, as well as explain how he obtained voicemail numbers and passwords.
Comedian Steve Coogan and PR consultant Nicola Phillips, a former employee of Max Clifford, have launched civil damages claims against News International, the former publisher of the News of the World.
A raft of information was contained in notebooks handed over by Mulcaire to the police after he was jailed for six months in January 2007 for illegally intercepting the voicemails of members of the Royal household.
Mulcaire, who was jailed alongside News of the World royal editor Clive Goodman, was said to have been contracted by the Sunday tabloid for "research assignments" from late 2001.
His appeal will be heard by the Lord Chief Justice, Lord Judge, the Master of the Rolls, Lord Neuberger and Lord Justice Maurice Kay in London, reports BBC News.
Last week, the high court heard claims that Mulcaire was involved in illegally tracking phone signals, in a process known as 'pinging', along with computer hacking.
However, the private investigator denied claims that he deleted the voicemail messages left on the phone of murdered schoolgirl Milly Dowler, leading her parents to think she was still alive.
Mulcaire's appeal case comes as the Leveson inquiry hears testimony from various sources as it investigates press ethics and standards following the phone hacking scandal.
Lord Leveson is currently hearing from the landlord wrongly accused of Joanna Yeates's murder, while singer Charlotte Church and former TV presenter Anne Diamond will give evidence later today.
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