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.
9. Rafa Benitez - 10/1
Without a club after leaving Chinese Super League side Dalian Pro. Would fall into the huge name category that will excite fans. Photo: Catherine Ivill
10. Enzo Maresca - 15/2
The left-field candidate. Coaching at Manchester City after a spell as West Ham assistant. Had a glittering career, playing in Serie A and La Liga. Photo: Tullio M. Puglia
11. Martin O'Neill - 7/1
Had great success in his first spell as Celtic boss. Photo: SNS Group Alan Harvey
12. Paul Lambert - 6/1
The former Parkhead ace's odds plummeted after he left Ipswich Town at the weekend. Photo: Alex Davidson