The Scot has become the centre of an internet storm after video footage of him appearing to making disparaging remarks about Rovers predecessor Sam Allardyce was published by a fans' action group.
That came against a backdrop of huge supporter unrest following the club's relegation from the Barclays Premier League.
A petition calling for Kean's removal containing almost 4,500 signatures was forwarded to Venky's by fans ahead of his arrival for what would ordinarily have been routine end-of-season talks this week.
The internet video is the latest controversy to hit Rovers after a letter from deputy chief executive Paul Hunt to co-owner Anuradha Desai, suggesting Kean be dismissed, surfaced in the media last week.
In the four-minute clip, apparently shot during Rovers' pre-season trip to Hong Kong last summer, Kean appears to be critical of Allardyce and predict a top-half finish as well as Carling Cup success.
He was in conversation with fans in a bar and unaware he was being filmed.
Press Association Sport understands Allardyce, who is now manager of West Ham, has instructed lawyers to initiate legal proceedings against Kean.
The BRFC Action Group, who posted the video on their website and YouTube, appear to be stepping up their campaign to oust Kean and the equally despised Venky's.
They pinpoint the club's takeover by the poultry firm 18 months ago as the start of their demise.
The group have now been granted a meeting with Sports Minister Hugh Robertson, facilitated by Blackburn MP Jack Straw, and the Premier League have also agreed in principle to meet them.
Group chairman Glen Mullan said: "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 have not been monitored at all, since the FA granted Venky's [status as] fit and proper owners.
"This will include agents' roles during their ill-fated tenure and lack of administration structure at the club."
Venky's said last week they had no intention of relinquishing Rovers and have never given any indication they would like to replace Kean.
Indeed, at times it has appeared that the only contact between Ewood Park and the distant owners is through Kean, who has made regular trips to India.
Despite that, former Accrington Stanley chairman Ilyas Khan has said he would front a consortium to attempt to buy Rovers if Venky's were willing to sell.
Khan told BBC Radio Lancashire: "If they were, I would be honoured if I could facilitate a transfer."