Motherwell do not anticipate having a new manager in place before Christmas.
Caretaker Gordon Young says he has no interest in succeeding Craig Brown, while captain Stephen Craigan does not think he will be considered.
And Fir Park chief executive Leeann Dempster told BBC Scotland: "I would not expect to have someone in place for this Saturday.
"If we were to have a manager in place for the match with Rangers on Boxing Day, we'd be doing very well."
Young, who is the youth development manager, will oversee Tuesday's rescheduled Scottish Premier League match against Hearts, while the Steelmen are up against former boss Brown's Aberdeen side on Saturday.
"We've had numerous applications and contact enquiries about the managers job, but we won't be rushed into making a decision," said Dempster.
"We've looked at the list and had our first discussion on the situation. We'll have another this afternoon and then we'll take a break from that and watch a game of football."
Experienced Northern Ireland international Craigan has been mentioned as a possible replacement for Brown.
However, the defender told BBC Scotland: "I don't think they'd be interested in me. I'll just keep playing football.
"I'm enjoying myself and I'm feeling as good and as fresh as I have done for a long time."
Brown and his assistant, Archie Knox, resigned their posts at Motherwell on Thursday evening and were confirmed in their new posts at Aberdeen on Friday.
On possible candidates to replace the veteran pair, vice-chairman Derek Weir: said: "We're looking for a blend of experience and people who can bring through young players.
"And we have a chairman [John Boyle] who likes to think outside of the box.
"We are busy drawing up a list from those who have applied and those who we think would be right for us."
Former Dundee pair Gordon Chisholm and Billy Dodds were immediately linked with the vacancy at Fir Park.
However, Dodds, who lost his job at Dens Park along with Chisholm when the First Division club entered administration in October, denied he had already discussed with anyone connected with Motherwell the possibility of taking over.
"I woke up to text messages and missed calls - all mentioning this story," said Dodds. "There's no story.
"I don't know where the story has come from.
"It's an attractive job for anybody, but if I'm going to get a job, it'll be off my own back.
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