They earlier lodged a petition with the Court of Session in Edinburgh seeking to recover items from News Group Newspapers who published the now defunct Sunday newspaper the "News of the World".
In it it was maintained that Mr Lennon's voicemail messages were illegally intercepted by private investigator Glenn Mulcaire in 2003, who was later jailed.
It also signalled Mr Lennon's intention 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."
The Celtic manager's senior counsel Alan Dewar QC told a judge today 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."
The senior counsel told Lord Bannatyne during a brief court hearing that the parties were agreed that the matter should be continued to next month.
Lawyers acting for the Celtic manager earlier brought the petition seeking an order under administration of justice legislation to recover documentation. Mr Lennon's address was given as care of a Glasgow law firm to maintain his personal security and it was said he had previously been the victim of an assault and had received an explosive package by mail.
It said Mr Lennon was "a famous professional football manager" and he had enjoyed a lengthy and successful career as a player with the Parkhead club and others before moving into management. He was also capped by Northern Ireland. It said there is and had been widespread media and public interest in his activities.
News Group published the high circulation tabloids "The Sun" and the "News of the World" before the latter stopped publishing.
"They regularly carried stories about the private lives of famous persons. They regularly carried stories about football, and in particular stories speculating about transfers of players between football clubs," it was said in the petition.
News Group was said to have invested "substantial sums in obtaining such stories".
In the petition it was said that Mr Lennon's voicemail messages were illegally intercepted by Mulcaire in 2003.
An entry in a notebook of Mulcaire showed Mr Lennon's address and phone number as well as other information of a personal nature, it was said.
It was said: "The petitioner does not meantime know the full extent of the interception of his messages."