Following Rovers' 4-0 home loss to Manchester City this afternoon, many Rovers fans chanted for Kean to resign from his position.
However, the 44-year-old has insisted that he has no intention of leaving his role and hopes that the Ewood Park faithful will change their point of view soon.
"We are in a difficult moment right now but we are not the only side that City will take three or four goals off," Kean told Sky Sports News.
"I hope [the fans] change their mind. I'm working hard and I know they're frustrated, but so am I."
Rovers remain in the relegation zone following the defeat.