Dundee chief executive Scot Gardiner claims the club have already been "swamped" with applications for their managerial vacancy after parting company with Barry Smith.
Former captain Smith's time at Dens Park came to an end on Wednesday following a string of poor results, which left the Dark Blues rooted to the bottom of the Clydesdale Bank Premier League.
His assistant, Ray Farningham, will remain at the club and could take interim charge of team affairs for Sunday's visit to Celtic.
Gardiner told the Scottish Sun: "We have already had people in touch about the job. In three hours we have been swamped with potential candidates.
"I have now got the task of identifying someone to take charge of the team."
Dundee are 15 points adrift in the SPL but Gardiner revealed the new manager will be tasked with keeping the club in the top flight.
He added: "The board hope changing manager can bring about a change of fortunes.
"We want to stay in the SPL and stay in the Scottish Cup.
"Nobody at Dundee is giving up on staying up or even getting to the cup final. Both those things are important to us, we are not calling it a day."