Supporters of the Parkhead club have been growing increasingly frustrated with the progress regarding a replacement for Neil Lennon.
John Kennedy has been in interim charge and has two games left of the campaign.
However, Celtic are due to start their season in 74 days with their first Champions League qualifying match.
Eddie Howe has been the strong favourite to take over the managerial job.
Celtic note they are in a “transitional period” with Dominic McKay replacing Peter Lawwell as chief executive but that “considerable planning and preparatory work” has already been undertaken.
“The club is working hard to complete the appointment of the new Celtic manager and relevant football staff and will be doing all we can to confirm this as soon as possible to our supporters,” the statement read.
"Rightly there will always be a huge appetite for information from our supporters – unfortunately we are not able to make regular public comment on this matter, but we fully understand and appreciate the need to complete this process as soon as we can.
"We also acknowledge and understand the frustration of our supporters during this process, but our objective of course is to ensure that we secure the best candidate possible to take the club forward and this is our focus. We will update all our supporters through our club communication channels as soon as we are able to.”
Lawwell and McKay are due to have met with the club’s “main supporters’ groups” with “engagement and dialogue” with fans “crucial”.
They have ensured fans that getting them back into the stadium is a “major priority”, working closely with “all the relevant authorities”, as they aim to bounce back from a turgid season.
The statement read: “We have not been able to deliver the kind of season we have become so used to and after such a sustained period of success, we sincerely understand the disappointment and frustration of our supporters – now we make it our objective to return the club to the top in the shortest possible timeframe.”