The BRFC Action Group have long called for the removal of Kean and claim owners Venky's, the Indian poultry firm, are not fit and proper persons to run the club.
Their campaign has been stepped up since the club were relegated from the Barclays Premier League amid scenes of unrest and protest at Ewood Park last week.
Blackburn MP Jack Straw has facilitated a meeting of the fans with sports minister Hugh Robertson next month and the Premier League have agreed in principle to meet them too.
A statement from the BRFC Action Group committee read: "We as a group of supporters, elected by its members, are disgusted that our club has been allowed to be pillaged with very little resistance from the regulatory bodies who should act in the best interest of the sport and supporters."
The action group's chairman Glen Mullan said in the statement: "This will give us an opportunity to put our case to the highest authorities and offer supporting evidence to why we feel that our club's activities has not been monitored at all, since the FA granted Venky's [status as] as fit and proper owners.
"This will include agent's roles during their ill-fated tenure and lack of administration structure at the club."
Many fans pinpoint the club's takeover by Venky's 18 months ago as the start of their demise.
Venky's sacked Allardyce soon into their stewardship and appointed Kean, who was the subject of demonstrations throughout this season's struggles.
Last week a letter from Rovers deputy chief executive Paul Hunt to Venky's calling for Kean's removal surfaced in the media.
Hunt has since left the club in what was described by Venky's as a cost-cutting measure following relegation.
The group's statement added: "In the last two weeks supporters' greatest fears have been realised as our club has lost its fight for Premier League survival, following the club's decision to keep manager Steve Kean in charge of first-team affairs.
"This is despite, according to, the well-publicised leaked letter by the DCEO Paul Hunt from December 2011 stating that Steve Kean had lost the dressing room, and the board had requested his removal as well as the wider supporter base."
Blackburn declined to comment.