The Rovers boss faces the axe after he failed to reach Singh's target of 16 points from the first seven games, despite Blackburn having their best ever start in the Championship. They are currently in third place on 14 points, following their relegation from the Premier League last season.
Singh told BBC Radio Lancashire: "Unfortunately, the momentum [of the speculation about Kean] built up so fast it was quite difficult to step in and react. We have people heading up different departments whose responsibility it is to step in but unfortunately it escalated at such a fast pace that before you know what happened, it hits you in the face."
He added: "It should not have been allowed to escalate like that but it did and the situation gets worse by the day. Financially now it is not a good situation because the fans are staying away. The club needs revenue to survive.
"I guess with having played seven games now I think it is a situation which is not a very pleasant one and I suppose it is my bosses, the owners of the club [Venky's], who have to make an assessment."
The 44-year-old has faced pressure throughout his time in charge at the club, with large numbers of fans calling for him to be fired, while owners Venky's had discussions about Kean's role over the weekend. Despite the uncertainty, Kean looks set to stay in charge for this weekend's fixture at Charlton.
The uncertainty around Kean's position comes as two supporters groups - the Blackburn Rovers Supporters Investment Trust (BRSIT) and Blackburn Rovers Supporters Trust (BRST) - have joined forces to launch the Rovers Trust - a new membership scheme whose goal is to own the Ewood Park club in whole or in part.
The new membership drive for the Rovers Trust has been launched in a bid to sign up Blackburn fans for a £10 annual membership fee to give the group credibility.
The membership push will then be followed by a share-raising plan modelled on the 'pledge scheme' first launched by BRSIT earlier this year. That scheme has seen almost £3 million pledged by supporters wanting to buy a £1,000 share in a new ownership model.
A target of £10m is being set by the co-chairmen, BRST founder Oliver Jones and Wayne Wild, one of the co-founders of BRSIT.