Thompson was once the Reds' youngest-ever player, making his senior debut under legendary mBill Shankly, when Liverpool drew 1-1 with Tottenham in the final game of the 1973/74 season.
He was just 17 years and 129 days old at the time and that record stood until 2010. Jack Robinson was the player to break Thompson's record, as he made his debut at the age of 16 against Hull in 2010.
Thompson only made two appearances for Liverpool, with his second coming in the 1975/76 campaign, in a UEFA Cup game against Real Sociedad.
Liverpool issued a tribute on social media, writing on Twitter: "We are deeply saddened by the passing of former player Max Thompson. The thoughts of everyone at the club are with Max's family and friends at this difficult time."
After leaving Anfield, the former central defender played for 15 clubs, but perhaps most notably at Blackpool, where he made just under 100 appearances between 1977 and 1981.
Once retired, Thompson went on to become a physiotherapist and was rehired by Liverpool in the early 1990s. He went on to work at Southport before his death.