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.
"You have got to tread with caution and if caution means taking a little bit more time than usual we'll take it," Singh told Sky Sports. But asked when an appointment would be made, he said: "Definitely by the middle of next week."
Singh revealed Rovers had already started interviewing candidates for the job.
He hinted that the club would favour a young up-and-coming manager, adding: "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."
Fulham manager Martin Jol says McKinlay might have been able to discuss the managerial vacancy at Blackburn had it been made clear he was the Championship outfit's number-one choice.
"They asked us a couple of days ago if they can talk to him and we said no," he said. "If you say yes it opens the door for other clubs to talk to my one of my staff members. There are always four to six other people involved, so why should I say yes?
"If I'm 100 per cent certain they'd take him I'd probably be a bit more positive.
"I need Billy. He's a good boy and is developing into a very good coach and manager.
"If they said, 'He's our number one choice', I'd probably tell them they can talk to him. But there are always big lists in football and I want Billy to stay. If I wanted someone I'd make a nice phone call, informal. With us it was formal - 'can we speak to him?' 'No'."
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- Billy McKinlay
- Tim Sherwood