The former Hoops midfielder has instructed lawyers to act on his behalf after he was given the news in a phone call by Lennon. The Scottish Premier League champions confirmed the Englishman's departure from the club on their website in a statement which claimed Thompson, 38, failed to attend a pre-arranged meeting with the Parkhead boss in Newcastle.
"We can also confirm that a meeting was set up between Alan Thompson and Neil Lennon on Sunday (June 3) in Newcastle," it read. "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."
While speculation abounds about the reasons for Thompson's dismissal, and whether or not it was at the behest of Lennon, it appears the relationship between the two men is over.
Former Celtic striker Andy Walker is surprised by Thompson's departure, three weeks after the SPL season ended with a title win for the Parkhead club. He told Sky Sports: "To be sacked over the phone is not ideal, but clearly something has boiled to the surface.
"I think it comes as a shock to most people. I don't know if this is a board decision or a decision taken by Neil Lennon. I am just very surprised. I was under the impression that Alan and Neil Lennon got on very well, they seemed very close.
"For the last number of weeks towards the end of the season when Neil Lennon was facing a number of SFA charges, Alan Thompson was the very public face of Celtic. He took on board all of the media duties, he was very accommodating and he is a very popular guy with the players and supporters, who held him in a high regard.
"So it is just very surprising that after three weeks after the season has finished that Celtic have chosen to take this course of action."
Thompson was brought back to the club in June 2010, when he was appointed as first team coach by Lennon alongside assistant manager Johan Mjallby, the three of whom were in the Celtic side which reached the UEFA Cup final in 2003.
Lennon's former Leicester team-mate Garry Parker was also recruited as a first-team coach which means Thompson's departure would not unduly deplete the backroom staff if he is not replaced.