Celtic are yet to draw up a list of candidates to replace Neil Lennon, according to their chief executive.
Lennon announced his decision to leave on Thursday, and Celtic great Henrik Larsson was quickly installed as favourite for the manager's job.
But Larsson's Swedish club Falkenbergs say he will remain in charge until the end of their domestic season in November.
And, speaking to Sky Sports News, chief executive Peter Lawwell said Celtic will take their time before making an appointment.
"There's nothing yet," he said. "We're just going to go into a selection process.
"We'll pull together a list of candidates, discuss it with the board and see if we can find a new manager. We're very, very early but we'll let you know as soon as we've got anything."
Celtic are due to enter the Champions League qualifiers in July, but Lawwell said: "We'll take as much time as it needs to get the right candidate. We've got a bit of time, so hopefully we'll get it right."
One man who would consider an offer from Celtic is their former midfielder Roy Keane, although he is in no rush to leave his current role as assistant to Republic of Ireland boss Martin O'Neill.
"I've got a job," Keane said. "There's always speculation when you're out of work or whatever, and obviously people might see this role as kind of part-time or whatever, but it keeps me busy. I enjoy it, I'm happy with what I'm doing.
"If somebody calls me I'll speak to Martin and the FAI and we'll have a look at it, but it's all speculation and the speculation comes from yourselves (the media). I don't think you've heard it from any club sources."
Who do you think will succeed Neil Lennon as Celtic manager?