The SPFL Premiership champions have not asked a manager to report to a director of football since Kenny Dalglish was removed from office 14 years ago, but the next manager might be faced with that scenario while also working with the help of one or two assistants.
Celtic made a move for Henrik Larsson, their iconic former striker, for one of the coaching roles but the 42-year-old told his Swedish club, Falkenberg, that he will not leave them before their season ends in November.
Whether Celtic change their current, traditional format - of a manager answerable to the board of directors - may depend on the seniority and conditions of the man they attract to take over from Lennon. But the director of football role was considered by the club in October 2011, in the opening months of Lennon's second full season. Both Gordon Strachan and Stuart Baxter were approached at the time, although neither was appointed and the proposal was put on the backburner until now.
Football development manager and chief scout John Park will take charge of football matters until a new manager is appointed and, like Lennon, he will have an input in the selection of the next manager. The club will take the time to consider the options, although the intention is to make an appointment long before most of the players are due back for the start of pre-season training on June 24.
Former Celtic player and Cardiff City manager Malky Mackay is admired by some on the board of directors but the views of major shareholder Dermot Desmond will be decisive. Desmond offered the job to Owen Coyle in June 2009, but he turned it down, preferring to stay with his newly promoted Burnley (Celtic appointed Tony Mowbray instead). Seven months later Coyle moved to Bolton but after their relegation from the Premier League and defeats in the Championship, he was dismissed in October 2012.
Coyle, 47, took over Wigan in the Championship last June but has been out of the game since being dismissed by them six months later. He also has current support from some within Celtic and could emerge as a serious candidate to take over as manager in the coming days.
Last night, he gave an interview with BBC Radio in which he described the opportunity as "marvellous", while playing down his chances of being offered it. He has been promoted to favourite by some bookmakers, but will be met with stern competition with chief executive Peter Lawwell also considering the merits of Oscar Garcia, Steve Clarke and Jackie McNamara.
The Swedish league season is 10 games old and Larsson is under contract to Falkenberg until the end of their campaign. Falkenberg's sporting director, Hakan Nilsson, said Larsson had told him a club had made direct contact with him, even though permission to do so was not sought from Falkenberg. "If that offer comes we will consider it then," Nilsson said. "[But] we are very happy to have Henrik with us. He has a contract with us and that contract is between us and Henrik, no one else."
Nilsson said he had not been told which club had contacted Larsson but, in any case, he was confident he would honour his deal: "He told me he has said no and I know him as a man of his word," Nilsson said. "We have no concerns about him leaving. I have no problem with the club who has spoken to Henrik. He had said no and therefore it is no question for us."
Another former Celtic player, Roy Keane, played down speculation linking him with a return to the club yesterday. Keane spent six months at Celtic in 2006 but said he would continue working as Martin O'Neill's assistant manager for the Republic of Ireland, and as a television pundit.
"I've got a job - I've got two jobs - I can't have another one," he said. "They are a brilliant club, an absolutely fantastic football club, one of the best in the world. But I have got a job. There's always speculation when you are out of work or whatever. People might see this [Ireland] role as part-time or whatever, but it keeps me busy, I enjoy it. I'm happy with what I'm doing and if somebody calls me, I will speak to Martin and the FAI and we will have a look at it. But it's all speculation."
Lennon and Johan Mjallby, his former assistant, reunited last night to spell out some of the potential benefits of overlooking Larsson's relative lack of coaching experience and handing him the manager's job.
His name has caught the imagination of a number of Celtic figures with former manager O'Neill and former players Chris Sutton, Aiden McGeady and Pat Bonner among those to have endorsed him.
Lennon insists Larsson, himself, will be best-placed to decide whether he has enough in his armoury to handle the pressures of the role. However, he was also an unknown quantity when taking over from Mowbray in March 2010 and has pointed out that Larsson's cv as a player stands comparison to any. "You would need to ask Henrik," said Lennon when asked if the Swede is ready to step into his shoes. "If he does, I am sure he would be a huge success. Why not? He has had a fabulous career as a player and is a very intelligent guy. He knows the game very, very well."
Larsson's coaching career has been a tough learning curve so far. He was appointed manager of homeland club Landskrona in December 2009 and given a contract extension after his debut season ended with them coming fifth in the Second Division. However, the following campaign proved to be a deep disappointment with supporters staging protests against him.
Larsson failed to win promotion once again in his third season, coming fifth, and left the club in November 2012.
Mjallby believes, however, that the main attraction in bringing his old team-mate back to Parkhead would be as a tool to revive attendances. "I can see the glamour thing with Henrik," said Mjallby. "He is quite recently into the job and doing quite well with quite a small team in the top league in Sweden.
"This is his first season in the top flight, but he is the King of Kings over in Glasgow and he would probably put bums back on seats as well."