The Millers are in their third managerial selection process in seven months following Neil Warnock's U-turn last week in deciding not to extend his short-term stay at the club.
Chairman Tony Stewart has been impressed with the candidates that have put themselves forward, indicating that some "big names" and a "higher level" of applicant are interested in the role.
Stewart and his board are likely to get on with creating a shortlist today, with interviews likely to follow in the week.
A host of names have been linked with the job, with Stuart Gray and Gary Bowyer thought to be under consideration while Alan Stubbs and Neil Lennon have also been mentioned.
Bowyer is the 7/4 favourite with the bookmakers, ahead of Gray, with odds shortening for Steve McClaren and Tony Mowbray after internet rumours over the weekend.
New Zealand manager Anthony Hudson, who was also linked to the post, is not thought to be in the running.
