The Scottish Premiership leaders will part company with Ronny Deila at the end of the season.
Leigh Griffiths has warned the Celtic hierarchy that failing to appoint a new manager quickly could have major implications on their chances of making an impact in the Champions League next season, the Daily Record reports.
The Hoops' current boss Ronny Deila will leave Parkhead at the end of this campaign, but with the Scottish Premiership title almost secured once again, the squad could be back training as early as mid-June in preparation for the qualifiers for Europe's premier competition.
And after watching Deila's men struggle to make an impact on the continent, Griffiths has urged the club's board to give the new boss the time needed to assess the squad to give them the best chance of improving their recent record.
"The new manager is not going to have a lot of time. The boys only have just over four weeks off then we are straight back into it," he told the Record.
"The qualifiers start in early July so he isn't going to have a lot of time."
Appointing a new manager as quickly as possible - provided that they still manage to make the right appointment to take the club forward - should enable the new man to put the squad together, along with any new signings, and allow them to build some chemistry in time for their first qualifier in mid-July.
Part of the reason that Deila struggled to win supporters over at the club was the fact that they failed to enjoy any of the famous European nights that Celtic Park has hosted so often in the past.
And while his struggles stretched over two seasons, Griffiths' warning that not appointing a new boss quick enough could scupper their hopes of making an impression in Europe next term should alert the board that getting the next man in place as early as possible could be crucial to determining whether his tenure starts on a better foot than Deila's did.