Rovers are looking for a new man to fill the Ewood Park hotseat after Steve Kean called time on his chequered 21-month reign as boss, stating that he was "forced" to step down and that his position had become "untenable".
Various names have been linked with Rovers, who are currently ninth in the Championship, over the last couple of days, with former striker Alan Shearer, ex-midfielder Tim Sherwood and much-travelled Swede Sven Goran Eriksson all linked.
Singh confirmed the club had been inundated with applications, telling Sky Sports News: "It has been a pleasant surprise despite the club having a lot of negative publicity. I would say it is an important job so I am pleasantly surprised there is a lot of people wanting to be a part of Blackburn Rovers.
"I would love to do it as soon as possible. It could be one week or three weeks. While we are in a hurry to appoint a new manager, we will not be rushed into it."
Despite the speculation, Singh refused to name any possible successors to Kean but suggested the list was full of quality. He added: "They are big names of course. Not so big names as well (are on the list), good coaches and it is a very interesting mix.
"There are a lot of big names from football and definitely there are big, big names on that list. In this moment of time, I will not release any names."