And it could be Henrik Larsson with Steve Clarke.
The former Hoops striker was the first name the club had on their list to approach when Neil Lennon decided to resign.
But, as SportTimes reported back on May 24, because Larsson is under contract with Swedish club Falkenberg until November, they had been told they would have to wait until then before he could move back to Paradise.
After Roy Keane removed himself from the running following discussions with major shareholder Dermot Desmond, Celtic appear willing to consider keeping the spot open for the iconic No.7 to become part of their new-look management structure.
In the meantime, they will press ahead with approaching other candidates on their list, with a view to bringing in one of them - most likely as manager - immediately.
That could be Clarke, who is still waiting for the call to speak to Celtic's movers and shakers.
The bookies continue to place the former West Brom boss at the top of their betting lists, where he has been since previous odds-on favourite, Keane, ruled himself out.
But anyone who has backed Clarke hoping for a quick pay out has been disappointed.
While he is spending some quiet time out of the public glare - all the while with his mobile close at hand - Celtic are understood to be reviewing all the possible candidates, and deciding on their next move.
Sources in Sweden claim Larsson has crept back into the frame, and his appointment - either as the boss or part of the management team - would sit well with most supporters.
Malky Mackay and Owen Coyle have remained in the list of candidates, along with another manager currently out of work, Michael Laudrup. David Moyes is an outside bet.
With the Southampton job vacant, along with that at West Brom, former boss Lennon is continuing to keep an eye on developments there as he completes his holiday ahead of travelling to Brazil to be part of the BBC's World Cup team.
Keane - who is expected to be confirmed as Paul Lambert's No.2 at Aston Villa, while also retaining his position as assistant to Martin O'Neill with the Republic Of Ireland - has withdrawn from the ITV pundits panel.
Another man not going to the finals is Celtic midfielder, Tom Rogic.
A persistent groin injury curtailed his appearances on loan at A-League club, Melbourne Victory.
He limped out of Monday's friendly against Brazilian club side, Parana and boss Ange Postecoglou decided he could not risk including Rogic in his squad.