The 21-year old centre-back looks set to depart Parkhead this summer after failing to become a first team regular since his 2009 move from Stockport County and there are a number of potential suitors who are keen.
Thompson's agent Peter Morrison said that his client will more than likely leave Glasgow during the current transfer window with the view of gaining regular first team football.
"I have spoken to Neil Lennon in relation to Josh and we are all in agreement that a permanent move away from the club would be in his best interests in order for him to progress his career," he told Sky Sports.
"He has played 21 times for Celtic in the SPL and has over 45 English league games under his belt so for a player his age he has a wealth of experience.
"Celtic have been fantastic with Josh and he has enjoyed his time with the club, but the time is right for a change and we are going to consider all the options open to him in the coming weeks."