Long-time favourite to become No.2 to Ronny Deila, John Collins, will have to confirm he still wants to be considered after being linked with a return to Hibs as Terry Butcher's successor.
The former Hoops midfielder is currently working part-time as a coach with the SFA. But, the man who has previously managed Hibs and Charleroi in Belgium, plus served as a Director of Football at Livingston, appears to have big decisions to make.
With Celtic's players scheduled to return for pre-season training a week on Tuesday, completing Deila's backroom team is becoming the priority for the new boss.
Lennon's assistant, Johan Mjallby, quit at the end of the season, while coach, Garry Parker, also elected to move on.
With Danny McGrain recovering from a heart attack, and scout Peter Houston taking over as manager of Falkirk, that currently leaves only goalkeeper coach Stevie Woods from last season's backroom Bhoys.
Youth team coach, John Kennedy - who yesterday represented the club at a press conference in Helsinki to promote the friendly against Tottenham Hotspur on August 2 - could be promoted into one of the vacancies, either temporarily or permanently.
But Deila is expected to appoint an experienced assistant with intensive knowledge of the game in Scotland.
Collins fits the bill, but the Hoops need to know his intentions as they push to fill the post as soon as possible.
Lennon has had talks with Arabian Gulf League club, Al Shabab Al Arabi, who placed him on their shortlist to replace Marcos Paqueta as coach of the Al Mamzar-based outfit.
He is expected to remove himself from the running for the £1.5million-per-year job as he would prefer to continue his career in England.
But Al Shabab vice-president, Mohammad Al Merri, confirmed: "We've not yet finalised on our direction, but he is one of the names presented to us.
"There are five coaches in the running. The other candidates are mainly South American, and we expect to confirm the new coach by the end of next week."
The squad Lennon has left behind at Parkhead is expected to be strengthened as soon as Deila has the chance to assess which areas are in most need of improving.
Work to bring in another striker was already underway before the change of management, and reports in Germany claim Borussia Dortmund's Julian Schieber is one man identified.
The powerful frontman has failed to make his mark since arriving for £5m from Stuttgart two years ago and Borussia indicated they are ready to cut their losses.
Celtic, West Ham and Wigan have all been credited with an interest in him. But the 25-year-old's representative, lawyer Robert Schneider, insists he has no knowledge of any link with the Hoops.
He said: "At the moment, Julian has a contract for two more years with Borusssia Dortmund. I don't know if he would consider moving to the UK. We've not spoken about it."
Teemu Pukki hopes he can convince Deila to give him a chance to prove he is worth a prolonged run up front in the Celtic side.
The Finnish striker endured a difficult first season at the club, but ended with seven goals.
He said: "I felt good towards the end of the season and was scoring goals and got more confidence in my play. This was good for me as it showed what I'm capable of.
"The first year with Celtic has been one of adapting for me. A lot has been different for me, but the end of the season was good and I found it easier to play."