Burnley hope to have chosen a new manager by the time they travel to Cardiff next weekend.
Joint-chairman John Banaszkiewicz revaled the Clarets have a shortlist of three or four names to replace Eddie Howe, who went back to Bournemouth last week.
"It's been quite an eventful week," Banaszkiewicz told the club website. "We have been up and down the country and interviewed over 15 managers so far.
"We are going to shortlist them to three and four and have second interviews, and we will get the rest of the board involved as well.
"It's quite difficult to pick the best one because there are three or four who are really capable and hungry for the job.
"But I hope we will have an announcement by next weekend in terms of who that candidate is."