On Sunday night, lawyers acting on Thompson's behalf claimed he had been dismissed in a phone call with manager Neil Lennon.
Celtic statement: "We can confirm that a meeting was set up between Alan Thompson and Neil Lennon on Sunday [June 3] in Newcastle.
"However, Alan refused to meet with Neil, hence the reason for the discussion being conducted by telephone.
"The matter is now in the hands of lawyers and, therefore, we are unable to go into any further details."
Thompson joined the club in June 2010, when he was appointed by Lennon alongside assistant manager Johan Mjallby following the sacking of Tony Mowbray.
Thompson's 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.