Glasgow born Hall first moved to Liverpool to go to university, and after graduating with a degree in mathematics, went on to play for the club 224 times between 1969 and 1976.
He then returned to the club in 1991 as head of its public relations and community department, a post he held until 2011 when he retired for health reasons.
Hall, who was 68, died on Thursday (16 July).
A statement on the club’s website said: "The thoughts of everyone at Liverpool Football Club go out to his family and friends at this sad time."
Others involved with the club have added their tribute, including Phil Thompson, the club's former captain who played alongside Hall.
So sad to hear of the death of my old teammate Brian Hall. What a great player but more importantly what a great man and friend he was.— Phil Thompson (@Phil_Thompson4) July 17, 2015