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.
1. Shaun Maloney - 16/1
The former Celtic player and aoch is assistant to Roberto Martinez with the Belgian national team. A popular pundit on Sportscene. Photo: SNS Group Paul Devlin
2. Roy Keane - 16/1
The Manchester United legend and former Celtic midfielder is a pundit for Sky Sports. Has been assistant to Martin O'Neill at Nottingham Forest and Republic of Ireland recently. Photo: SNS Group Craig Williamson
3. Michael O'Neill - 16/1
O'Neill took over Stoke City after a hugely successful spell with Northern Ireland. Photo: SNS Group Craig Williamson
4. Jesse Marsch - 16/1
The Red Bull Salzburg boss is highly thought of. A former US international, he has managed Montreal Impact, New York Red Bulls and been assistant at RB Leipzig. Photo: Andreas Schaad