Rovers, lying 17th in the Championship, sacked Henning Berg on Thursday after only 57 days in charge and a dreadful run of results.
"There have been no appointments made, nor will there be in the immediate future," Singh told BBC Radio Lancashire.
Reserve team coach Gary Bowyer will take charge for Saturday's game against Barnsley at Oakwell.
Berg replaced Steve Kean on 31 October but the club won only one of their 10 matches during his time in charge.
Assistant manager Eric Black, coach Iain Brunskill and goalkeeping coach Bobby Mimms also left the club.
Former Blackburn managers Mark Hughes and Kenny Dalglish have been linked with the vacancy, while former Aston Villa first-team coach Kevin MacDonald is also likely to be a candidate.
Singh approached MacDonald in November about the possibility of him becoming Berg's assistant.
Former Hull City manager Phil Brown has already expressed an interest in the job.
Brown has been out of management since his departure from Preston North End in December 2011.
The 53-year-old was expected to take over at Hartlepool United in November, but negotiations stalled and the club appointed John Hughes instead.
"My CV is certainly going in - I think it is a fantastic opportunity for somebody," Brown told BBC Radio 5 live.
But the obvious candidate looking from the outside in, is surely Billy Davies? The fiery Scot has taken three Championship sides - Preston, Derby and Nottingham Forest from relatively poor positions and achieved the play-offs with each - getting Derby to the Premier League by beating West Brom in the first play-off final back at Wembley.
One stumbling block to this may be the fact that former Preston Chairman, Derek Shaw is now managing Director at Blackburn and it is well documented that Davies did not depart Preston on the best of terms during Shaw's tenure.
But in terms of proven ability there is not another available manager that we can see with Davies' pedigree.