Murray extended the invitation to the late pop star's mother to "answer any questions she might have."
The invitation came Tuesday night via a statement released to CNN through Murray's lawyers, Valerie Weiss and Michael Flanagan.
"I've been told that she has a desire to speak with me before she departs this life," Murray said. "Seeing that she is up in age and in questionable health, and the fact that she is the mother of a very dear departed friend, it would give me great pleasure to sit with her one on one and answer any questions she might have."
Murray, who is serving time in a Los Angeles County jail after he was sentenced to four years for involuntary manslaughter in Jackson's death, said he would put Katherine Jackson's name on the visitor list.
"It would put her at peace," he said in his statement. "I would do that truly out of concern for her and altruistic love and concern for others. I want to see her. I do not want Mrs. Jackson to suffer. She remains as dear to me as my own mother, unbeknownst to her."
Murray's offer comes amid an ongoing feud among members of the Jackson family that has engulfed Katherine Jackson and the late singer's three children.
"Although I am not permitted to see the news in jail, there are times when intermittent snippets are seen before a channel change occurs," Murray in the statement. "I recently saw Katherine Jackson in one of those snippets. She appeared to be extremely sad. I also heard she is having a difficult time."
Reps for Katherine Jackson did not respond immediately to ABCNews.com's request for comment, but one told CNN that it was doubtful she would accept Murray's offer.