Sunday's match at home to Tottenham will see an organised group of supporters march to Ewood Park prior to kick-off and stage a 45-minute sit in after the match.
It will be third successive home game fans have called for Kean to be sacked with the team bottom of the Barclays Premier League.
Keeping the faith: Kean has hailed the togetherness of the squad
Questions about the protest were ruled off-limits at the manager's pre-match press conference but that will not prevent further debate about Kean's position.
This week striker Ayegbeni Yakubu insisted all the players were fully behind Kean, who has won just six of his 29 league matches in charge, and the Rovers boss welcomed that public support.
'It is nice when your players give you a little bit of backing,' said the Scot. 'I know what my players are like - they are a great bunch of lads who work their socks off.
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'We will go out and be fully committed to getting three points against Tottenham but it is always nice when the boys voice togetherness, not just about me but about each other.'
Organisers of the protest claim their voice is not being heard within the club - not necessarily over the future of Kean but generally - despite a group being invited to India earlier this month to meet owners Venky's.
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The supporters have no desire to protest but while the club continues to have no dialogue with supporters we feel we have little choice,' Glen Mullen, one of the organisers, said in a statement.
'The fans want unity from both the club and management to include the unity of supporters.
'We are very concerned we find ourselves staging a protest for the third home game on the trot and feel the club and management team could have brought these protests to an end if they had shown a willingness to communicate.'
Rovers have won just once this season, at home to Arsenal, and have just five points from eight matches. So far a gap has not opened up at the bottom - Rovers are only three points off 12th - but Kean knows their bad run cannot continue for too long.
'We are at the stage in the season now when we need to put together performances for the full 90 minutes and get points on the board,' added Kean.
'You keep things upbeat by getting the lads out to work because they enjoy training and working on things.
'There is a balance to be struck. No matter what the result is there is very seldom the perfect game and there is always something to work on.'
Utility player Martin Olsson admits the players cannot afford to get down about results or forthcoming fixtures - they head to Norwich before Chelsea visit.
'It is not good of course but we have to think about the positives,' said the Swede.
'If we get three wins in a row we will be up there straight away.
'We have to think positively not negatively because if we do that we will just stay down there. 'We have to move forward and think of a win on Sunday.
'Tottenham and Chelsea are the next two home games. They are tough games but we have done it before.
'We are going to give them a game and give 100 per cent, that is all we can do.'
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