Kilmarnock want a "highly-experienced" manager to replace Steve Clarke and will draw up a shortlist by the end of the week, says owner Billy Bowie.
The Rugby Park board will convene on Thursday to sift through the candidates and set up two days of interviews.
Clarke left the Scottish Premiership club last week for the Scotland job.
Bowie said Clarke will be "a very hard act to follow" but that he has been "very encouraged" by the calibre of those applying.
However, he added that the candidates who have already made themselves known are of "a very good level" and are "from all over".
Alex Dyer will stay on as assistant manager role, while also helping Clarke with Scotland.