The former midfielder joined the club in June 2010, when he was appointed by manager Neil Lennon alongside assistant manager Johan Mjallby following the sacking of Tony Mowbray.
Thompson is a former Celtic player and a former team-mate of Lennon's.
His lawyer, Margaret Gribbon, of Glasgow-based Bridge Litigation, said in a statement: "I can confirm that I have been instructed to act on behalf of Alan Thompson following his dismissal by Celtic FC.
"Alan was informed of the decision to terminate his employment with immediate effect in a telephone conversation with the club manager Neil Lennon."
Thompson played for the Glasgow club between 2000 and 2007, winning four Scottish Premier League titles and three Scottish Cups.
Nobody from Celtic was immediately available to comment.