Frontrunner Eddie Howe must give a final answer to Celtic urgently or the club should move on insists Alan Stubbs.
The Englishman is the number one target with fans eagerly awaiting an announcement over Neil Lennon's successor.
The Parkhead club put out an update on Friday as they acknowledged fan concerns about the managerial situation as John Kennedy holds the fort.
Stubbs doesn't believe that Dermot Desmond, Dominic McKay and Peter Lawwell should be hanging about and waiting on Howe.
The former Celtic Park defender insists the former Bournemouth boss must have a final answer and move on.
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He told Football Pass UK : "Celtic have made Eddie Howe their number one target, which is fine, but we were talking about this six or eight weeks ago and we are in a position where we are no further forward.
"If I was a Celtic fan, well I am a Celtic fan, but I'd be very concerned. The longer this goes the more likely that this is going to be a no. and Celtic are going to have to move on to someone else.
"I don't know what the delay is. If it's Eddie Howe waiting to see what else is on the table, I don't think the club should be putting themselves in that position.
"This is Eddie Howe's biggest challenge he will ever face. He has done great at Bournemouth, but lets make no mistake, Bournemouth is not Celtic Football Club. Celtic Football Club is a huge club worldwide. Bournemouth is looked on as a nice little club, Celtic is a huge club.
"If he is a success here he will go on to manager a huge club after Celtic.
"I don't know why he hasn't accepted by now, and if I was the Celtic board I'd be very nervous.
"There is obviously a lot of frustration, the Celtic board have come out and said they understand the fans are frustrated, and they are asking for patience.
"You don't get time in football. Football doesn't stand still.
"Now it's a frank conversation. 'Eddie, we need to know, are you going to become Celtic manager? Yes or no. Otherwise we move on.'
"It's a huge job to do at Celtic. Dominic McKay has started early and he will want a manager appointed as soon as possible.
"I think this could be one of Celtic's biggest challenges in terms of transfers.
"There are more players going out than staying, and there are question marks over even the ones that are staying. There is a lot of work to do."
You can watch Stubbs' interview with the Football Pass via the video player above.