Rovers will play host to fellow strugglers Bolton Wanderers on Tuesday in what is already being billed as a relegation six-pointer.
Just one place and a solitary point separate the two sides at the foot of the Premier League table at present.
Kean and his opposite number Owen Coyle know there is little margin for error heading into a pivotal game for both clubs.
It is, however, Kean who is under the most pressure, with Blackburn supporters and the local newspaper calling for his head.
He has given no indication that he plans to step down, though, and says he continues to have the full support of Rovers’ owners Venky’s.
“I spoke with the owners for about 45 minutes yesterday (Sunday),” Kean told Sky Sports News HD.
“We had a real good conversation, mentioning again the health of some of the players because we have got a few that are falling at the moment.
“We will look forward to the transfer window opening and see if we can get a few bodies in that can hit the ground running straight away and make an impact.”
Asked if the owners had issued a win or bust ultimatum ahead of the Bolton game, Kean added: “No, not at all.”
The Scot is fully aware that he needs to turn things around at Ewood Park and has called on the supporters who continue to question his reign to get behind the team on Tuesday.
“Stick with us. With a game that is as important as this, stick with us,” he said when asked if he had a message for the disgruntled fans.
“When we scored (in a 2-1 defeat by West Brom on Saturday), I felt the momentum swung in that game and they were with us then.
“Obviously when you get a late goal against you it’s disappointing, we were all disappointed. But if they could stick with us for this game, I think it could make a massive difference.
“I’m not trying to pretend that I don’t understand the magnitude of this game. I’m not enjoying where we are in the table.
“But when I look at the players and I get out on the training ground and they are giving a response, they are certainly behind what we are trying to do. That gives you a massive boost.”