Major Celtic shareholder Dermot Desmond feels that the Bhoys need to secure a "great manager" as they are a great club and is hopeful an appointment will be made within the next five days.
Norwegian tactician Ronny Deila has departed his role at Parkhead after delivering successive Premiership titles during his two years at the club – and now Celtic are moving to name his replacement.
The Bhoys have held talks with former Liverpool manager Brendan Rodgers and ex-Cardiff City boss Malky Mckay. David Moyes, Neil Lennon, Paul Lambert and Roy Keane have all also been mooted as potential contenders for the job.
Desmond thinks progress will be made quickly and he is sure that Celtic must be targeting the very highest calibre of manager.
He said on Sky Sports: "I can say we've talked to a lot of managers, all very good.
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"We're excited about the candidates that we have and hopefully in the next four or five days we'll be able to make an announcement.
"We'd like to think Celtic is a very big club and it needs a great manager to manage such a great club, so we're looking for that type of person", Desmond added.
Celtic failed in Europe during Deila's time at the club, not managing to reach the Champions League group stage and then this season struggling to make an impact in the Europa League.
Deila's successor will be tasked with changing that, while also renewing hostilities with Old Firm rivals Rangers, who won promotion from the Scottish Championship this season.
