The Scottish Premiership side are looking for Ronny Deila's replacement.
Chris Sutton has predicted that Celtic will appoint either Paul Lambert, Malky Mackay or Neil Lennon as their next manager as he believes that the current structure at Parkhead would put some of the bigger names off the move, the Daily Record reports.
The Hoops are looking for a new boss with Ronny Deila set to step down at the end of the current campaign. And Sutton explained that the influence that he believes chief executive Peter Lawwell has at the club means that one of the trio are the most likely to be given the task of succeeding the Norwegian.
"An old-school manager would want to run the club and that's why if I was a betting man I'd go and put a wager on a Paul Lambert, Neil Lennon or Malky Mackay. Someone who Peter [Lawwell] will be able to manage," he told the Record.
If the club is run as Sutton suggests, then perhaps it would not be a surprise if one of the three was given the role. All three have endured difficult times as managers lately so would undoubtedly view a move to the Scottish Premiership champions as a huge step forward and thus, may not care too much about the structure in place.
Lambert has recently stepped down after an unspectacular spell as Blackburn boss, having previously been present for part of Aston Villa's plight.
Meanwhile, Mackay's most recent spell as manager saw him unable to take Wigan out of danger before departing shortly before their relegation was confirmed, and Lennon's time at Bolton ended in a similar manner this season as he left the Trotters less than a month before they were officially relegated from the Championship.
And perhaps that desire to enhance their reputation at a club which has dominated the Scottish game over the last five years is the reason that Sutton believes that they would be willing to work in a structure that may put some of the bigger names off.