Since Kean took over from Sam Allardyce, Blackburn have played 33 league games and picked up just 23 points.
They are currently bottom of the Premier League with just one point ahead of Saturday's lunchtime clash with Arsenal.
Fans have launched an online petition and plan to march to Ewood Park, demanding owners Venky's sack Kean.
It is thought that they will also demand the re-instatement of Mark Hughes, who is jobless since leaving Fulham this summer.
Organiser Glen Mullan told the Daily Mirror: "The numbers look like hitting the 1,000 mark so the fans are keen to have Steve Kean removed.
"It's going to be a peaceful march, but we want to make our point and there will be banners made. It's about time the owners listened to the fans.
"We want someone who is experienced and can relate to the fans."