They had previously lodged a petition with the Court Of Session, Edinburgh, seeking to recover items from News Group Newspapers, which published the now defunct Sunday paper the News Of The World.
The petition claimed Mr Lennon's voicemail messages were illegally intercepted in 2003 by private investigator Glenn Mulcaire, 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.
Alan Dewar, QC, the Celtic manager's senior counsel, told judge Lord Bannatyne that an undertaking had previously been given and searches based on it had taken place.
Mr Dewar said: "A degree of material has now been produced and it is being assessed."
The brief court hearing was told the parties were agreed the matter should be continued to next month.
Mr Lennon's address was given as care of a Glasgow law firm to maintain his personal security. It was said he had previously been the victim of an assault and had received an explosive package by mail.
The petition said Mr Lennon was "a famous professional football manager" who had enjoyed a lengthy and successful career as a player with the Parkhead club and others before moving into management.
It said there was widespread media and public interest in his activities.