Principal shareholder Desmond has provided an update on the search for Neil Lennon’s replacement following the Northern Irishman’s departure earlier this year.
Current interim boss John Kennedy, Manchester City youth coach Enzo Maresca and former Sheffield United manager Chris Wilder are the frontrunners, according to the bookmakers.
Desmond told the club’s website: "As with any key appointment at Celtic there is a process which involves research, investigation, interviewing and negotiation. This process is underway and is taking place privately and when complete, the board will make a public announcement.
“The chairman Ian Bankier, Peter Lawwell and myself take a lead in the process, and naturally, the incoming CEO will also participate. Any decision made will require board approval."
Regarding the type of manager the club would like to appoint, Desmond remained coy on the subject.
“We are mindful of the fact that there is a huge amount of interest and speculation among our supporters and the press,” he said.
"However, we have to respect the privacy of potential candidates and the integrity of the process, and so I think it would be inappropriate to make comment on the type of candidate we are looking for.
He added on his hopes for next season: “That we recruit a manager that plays football the way that all Celtic supporters want and that we give that manager the time to implement their own plans. After that, I am sure much more success will follow.”