John Kennedy, who has been Lennon’s long-time assistant at Parkhead and also worked under Brendan Rodgers, will hold the fort until a permanent successor is found.
Steve Clarke leads the bookmakers’ markets while names such as Eddie Howe, Rafa Benitez and Jack Ross have done the rounds in recent months.
However two intriguing, lesser known names have been present among the runners and riders on bookies lists – Enzo Maresca and Leonardo Jardim.
Less is known about the duo than the other, perhaps more glamorous names, among the high-profile bosses who have been touted and suggested.
So who are they and why have they been linked?
If Celtic are looking to change the club structure and pursue a head coach and director of football model with recruitment handled elsewhere, developing and nurturing talent as well as tactically leading the first team will be a strong suit and key performance indicator.
The pair have strong ties to developing talent in their most recent jobs – and in dealing with some big name players and clubs.
We delved deeper into the background of Leonardo Jardim and Enzo Maresca.
Of the pair in focus, Jardim has the higher profile as a manager – and it’s clear to see why. Names like Sporting Lisbon, Olympiakos and AS Monaco are not inconsequential clubs in European football terms.
Out of work since departing Monte Carlo for a second time in 2019, the Venezuelan-born boss has experience of defying the odds in Europe and domestically.
Monaco’s run to the semi-finals of the Champions League in season 2016-17, under his stewardship, was commendable but perhaps winning the Ligue 1 title against the riches of Paris Saint-Germain trumped that achievement four years ago.
That European pedigree will certainly be attractive to Celtic who have flattered to deceive on the continent over recent seasons.
His domestic duel with PSG, not to forget Lyon and Marseille, will not be too dissimilar to the pressure and expectation levels in Scotland – success in it shows potential.
Jardim is a coach, not a former player and has developed through the grades at lower levels in Portugal before scaling the heights on the European stage - not unlike another with Portuguese background, Jose Mourinho.
Still only in his 40s he is seen as one of the bright new coaches and tacticians coming to the fore - yet has been out of work more than a year since leaving Monaco.
He also has experience in bringing through young players into his Monaco side – Kyllian Mbappe and Bernardo Silva to name but two success stories.
Uncovering rough diamonds to be polished and young talent to be cultivated, utilising the Celtic Academy to follow Callum McGregor and Kieran Tierney’s path to the first team and beyond, is a key quality for any new man at Celtic Park.
Tactically astute which might suit the European front, he is - again not unlike Mourinho - seen as a naturally pragmatic manager, willing to prioritise success and stability over style and substance.
That is not to say he is a negative manager, far from it - how could he be with previously mentioned Mbappe, Silva and attack-minded players like Benjamin Mendy, Joao Moutinho and Thomas Lemar in his sides?
Utilising bright young talent would suit the Celtic fans and his record for developing players adds weight to his tactical argument – and who is to say he would remain pragmatic at the helm of one of the top sides in Scotland?
Jardim might have the managerial background, but Enzo Maresca has significant stamps on his football passport as a player and coach too.
As a player he starred in the midfield of Juventus and Sampdoria, and for the past six months the Italian has been at Manchester City leading the club’s young talent progression as head of Elite Development Squad.
Prior to that he was assistant manager to former City and Real Madrid coach Manuel Pellegrini at West Ham United and has spent time as assistant manager at Sevilla too.
Without extensive managerial experience it’s hard to judge Maresca – although that might not be a bad thing.
Celtic are believed to be developing a director of football based model with a head coach taking control of team affairs and a recruitment department identifying and bringing players to the club. That might well suit a manager, or a head coach, with Maresca’s background, particularly at City – a club Celtic have had frequent dealings with over recent years in Jeremie Frimpong, Olivier Ntcham and Patrick Roberts deals.
Recently they have been linked with Manchester City’s Fergal Harkin too, which would lend more weight to the Maresca suggestion – if either was to prevail.
Again, it’s hard to decipher for a rookie manager – however he is credited with a tactical masterstroke in West Ham’s midfield which saw the Hammers upset Chelsea for their first win at Stamford Bridge in 17 years and addressed an eight-game winless streak under Pellegrini last season.
The Italian has previously said he is keen to make the step into the hot-seat as a number one – but only after serving his time as an assistant and learning the ropes.
Having assisted Pellegrini in the EPL and at Sevilla through to the Champions League quarter finals there’s a big background there before you even reach Manchester City and his role in the structure there – but is it a solid enough foundation to make the step up into his first top job at Celtic?