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Brendan Rodgers and Celtic parted ways last month, with Martin O’Neill stepping in on an interim basis.
O’Neill has overseen three wins and one defeat so far, but the club are keen to finalise a permanent appointment as soon as possible.
Ange Postecoglou is considered highly unlikely to return as Celtic’s next boss, while Kieran McKenna and Craig Bellamy are among the leading candidates to replace Rodgers.
It is understood that several targets had already been identified ahead of an anticipated summer change, but Rodgers’ shock departure has forced the club to accelerate their search.
Ipswich Town head coach McKenna is a figure Celtic admire greatly, though he remains under contract at Portman Road until 2028.
Meanwhile, Wales manager Bellamy – who had a brief loan spell at Celtic in 2005 – is another name firmly on the club’s radar.
The Scottish champions have also been monitoring Bodo/Glimt boss Kjetil Knutsen and Club Brugge head coach Nicky Hayen, though securing either mid-season may prove difficult.
Former Liverpool striker Robbie Keane and ex-coach Damien Duff are also being considered.
Keane, currently managing Ferencvaros, has disclosed that he remains focused on his work in Hungary despite speculation linking him with a return to Glasgow.
He led Ferencvaros to the Hungarian title last season and has steered them to third place in their Europa League group, with three wins and a draw.
Speaking at a coaching conference in Hungary, Keane echoed his previous stance regarding the Celtic job, insisting he has learned to block out external noise about his future, a skill he developed during his playing days.
Keane said: “As a player, they wrote that I would sign here or there, but it’s the same – there is nothing you can do about that, I am only and exclusively focused on my work here.”
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