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The action comes in relation to unguarded comments made by Kean about Allardyce to supporters while secretly being filmed last summer.
The four-minute video, apparently filmed during Rovers' pre-season trip to Hong Kong, was released on the internet overnight.
In the video, Kean makes comments which appear to be critical of Allardyce during his conversation with fans in a bar.
In footage in which expletives are used, Kean also appears to predict Rovers will finish in the top half of the Premier League and win the Carling Cup.
Kean has been a hugely unpopular appointment since being promoted from within to replace the sacked Allardyce in December 2010.
There are various views - was Kean gullible telling his feelings to supporters? Should the supporter broadcast what was obviously an "off the record" conversation?
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If you want to see a tear-jerker following relegation ... look at this video showing a poor 4-year-old trying to console her dad ...