His counsel told a hearing at the Court of Session in Edinburgh yesterday that they are sifting through material after Lennon's phone numbers were allegedly found in the notebooks of a private investigator.
Mr Lennon's legal team are seeking to recover items from News Group Newspapers, which published the Sunday tabloid newspaper until its closure in July 2011.
They maintain that the manager's voicemail messages were illegally intercepted by private investigator Glenn Mulcaire in 2003, when Mr Lennon would have been a player with the Glasgow club.
Mr Lennon's team intend to start legal proceedings against News Group for a claim of damages over the phone hacking.
It said: "The petitioner (Mr Lennon) intends to commence proceedings against the respondent in this court seeking damages for the illegal interception of his voicemail messages."
Mr Lennon's senior counsel Alan Dewar, QC, told a judge yesterday that previously an undertaking had been given and searches based on it have taken place.
Mr Dewar said: "A degree of material has now been produced and it is being assessed."
He told judge Lord Bannatyne during a brief court hearing that the parties were agreed that the matter should be continued to next month.
Lawyers are seeking an order under administration of justice legislation to recover documentation.
A petition before the court stated that News Group, which also publishes The Sun, said both papers regularly carried stories about the private lives of the famous and speculative reports about football transfers.
It follows Operation Rubicon, a Scottish police inquiry into alleged phone hacking north of the Border. Up to 50 detectives were working on the inquiry at its height in 2011.