Steve Kean resigned to end his troubled reign at Ewood Park on the eve of last month's 1-1 draw at Charlton and a host of high-profile names were immediately linked with the job.
Caretaker boss Eric Black will search for his first win in charge at the fifth time of asking against Sheffield Wednesday in the Championship on Wednesday night and Singh, overseeing the recruitment process on behalf of owners Venky's, insists he will not be rushed into an appointment as Rovers look for an instant return to the top flight.
"It has been a very, very difficult three weeks - difficult in that we have to make a quick decision but, at the same time, we cannot rush into making such a decision because of recent history," he said.
"That means taking time and, yes, I do understand that we need to make an appointment but it cannot just be any appointment because obviously after what happened we've got to tread very, very carefully. I would like to appeal to the fans; do not react to what you read in the papers or what is rumours - do not react to that.
"I am taking everybody's emotions into consideration. The fans have been through difficult times and the last thing I want is to put fans through more anguish. So give me more time now, rather than all of us rush into a decision and we all suffer together."