Chief executive Gavin Baldwin met with the club's owners on Monday to sift through the applications and following that meeting a four-man shortlist was drawn up.
Rovers will not be disclosing the names on that list but the club did say they expect the interview process to be completed early next week and an announcement on the new manager will then be made "as soon as possible".
"There has been a huge amount of interest for the position of first team manager at the club," said Baldwin via a statement on Doncaster's official website.
"The quality of applicants has been pleasing and we feel that that the four candidates that have been shortlisted are the best suited to Doncaster Rovers.
"We set an 18-point criteria outlining the qualities which we believe are required to help move this club forward.
"The interview process has now begun and we hope to have concluded the process by early next week. Once a decision has been made, we will look to unveil our new manager at the earliest possible convenience."
Doncaster are looking for a successor to Brian Flynn, who guided Rovers to the League One title this season after taking over from Dean Saunders in January following his departure to Wolves.
Flynn was handed the reins on a caretaker basis before being given a contract until the end of the campaign and the former scout will now undertake a director of football role.