Neil Lennon will work with assistant Johan Mjallby and coach Garry Parker through the pre-season before deciding if another man has to be brought in.
Senior sources within Parkhead have confirmed the decision to remove Thommo from the Hoops management team was for footballing reasons.
Lennon made the final call and is understood to be of the view that, despite bringing the SPL title back to the club for the first time in four years, the structure put in place after he replaced Tony Mowbray in 2010 had not worked out as well as he had hoped.
Now, when the players report back on July 2, they will be met by only Lennon, Mjallby and Parker, plus keeper coach Stevie Woods.
Several names have already been linked with the first-team coach's position including ex-Liverpool assistant coach Stevie Clarke.
But Lennon wants to see if his plans for coaching the first-team squad can be accomplished with a reduced management team.
If the pre-season games show this is not feasible, the situation will be reviewed.
It is further confirmation Lennon will not allow anything – includ-ing long-term friendship – stand in the way of him improving the club.
It is a disappointing ending to Thompson's return to the club where he played from 2000 until 2007, working under both Martin O'Neill and Gordon Strachan.
Thompson has now instructed lawyers to act on his behalf and Margaret Gribbon, of Glasgow-based Bridge Litigation, said: "I can confirm 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."
Celtic hit back by releasing their own statement explaining the sacking took place by phone because Thompson failed to meet with Lennon.
It read: "We can confirm Alan Thompson has left the club. We can also confirm a meeting was set up between Alan and Neil on Sunday 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."