A number of loan players will depart with some of the club's star players likely to interest clubs from England and around Europe. There has been talk of a director of football being brought to the club, something talked up by former boss Brendan Rodgers.
John Kennedy, who worked under Rodgers and then Neil Lennon, is currently in interim charge and won his first game at the weekend, defeating Aberdeen 1-0 at Celtic Park.
Many Celtic fans will be looking for a more prestigious name to be appointed and there have been some big names touted who will bring a variety of styles to the club.
Scroll down and click through for the latest odds supplied by Betfair on the most likely candidates to replace Neil Lennon permanently.
13. Frank Lampard - 5/1
The Chelsea legend was relieved of his duties at Stamford Bridge earlier in the season. Would make an interesting battle with Steven Gerrard. Photo: Julian Finney
14. Roberto Martinez - 5/1
The former Wigan and Everton boss is set to lead Belgium at the Euros this summer after guiding them to a third-place finish at the World Cup in 2018. Photo: Kevin C. Cox
15. Steve Clarke - 5/1
Guided Scotland to their first tournament since 1998. Photo: Alan Harvey - SNS Group / SFA
16. Sean Dyche - 4/1
Dyche has been in charge at Burnley since 2012 and is approaching 400 games. Photo: Alex Livesey