Sources say the church will reap about $8 million for the four-level heritage building, on the corner of Flinders Lane. It paid $720,000 in 1980.
The church, whose members include Kirstie Alley, Tom Cruise and Lisa Marie Presley, is restoring and renovating the former Sisters of Mercy College in Ascot Vale.
It is expected to move to the premises on Mt Alexander Road before the end of the year.
Jones Lang LaSalle’s Damien Steele is believed to be involved in the sale, but he declined to comment.