Rovers have had approaches for Fulham first-team coach Billy McKinlay and Tottenham counterpart Tim Sherwood rejected as they look for a replacement for Steve Kean.
The Championship outfit have been without a manager since Kean's resignation on 28 September, with Eric Black currently in caretaker charge, but Singh insists the wait is almost over.
"You have got to tread with caution and if caution means taking a little bit more time than usual we'll take it," he said on The Footballer's Football Show on Sky Sports 1.
Asked when an appointment would be made, he said: "Definitely by the middle of next week."
Former Tottenham manager Harry Redknapp has been linked with the position but Singh, who has already started interviewing candidates, hinted that the club would favour a young up-and-coming manager.
He said: "This group is obviously the most interesting one, because you've got to look, you've got to find, you've got to search, so that is possibly why it has taken more time."
While Singh remains tight-lipped on the Redknapp link, caretaker coach Eric Black admits the appointment of such a high profile coach would be quite a coup for Rovers.
He said: "He is a fantastic manager. You are right up at the top echelons of management.
"He'd be a sensational appointment for Blackburn."