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.
5. Carlos Queiroz - 14/1
Currently without a team, the 67-year-old has had a nomadic managerial career. Spells in Japan, UAE, America as well as managing Real Madrid, South Africa, Iran, Portugal and most recently Colombia. Photo: Hector Vivas
6. Damien Duff - 14/1
Had been part of Neil Lennon's coaching staff before stepping down to take a role in the Republic of Ireland set up under Stephen Kenny before stepping down earlier this year. Photo: Bill Murray - SNS Group
7. Mark Hughes - 14/1
Hasn't had a managerial job since Southampton in 2018. Photo: Michael Steele
8. Jindrich Trpisovsky - 14/1
Hit the headlines recently by guiding Slavia Prague to a win over Leicester City in the Europa League and will face Rangers. Has won the Czech title the past two seasons. Photo: MICHAL CIZEK