The West Ham United manager has reportedly instructed his solicitors to look into a video clip of his Ewood Park successor criticising him that was published on the internet
The 57-year-old is said to be unhappy with his former colleague after a video was published on the internet which showed Kean criticising Allardyce and questioning his integrity.
A spokesman for Allardyce told the BBC: "He has issued legal proceedings against Steve Kean and Blackburn Rovers but is unable to comment further at this time."
During Blackburn's pre-season tour of Hong Kong in 2011, Kean was speaking to supporters in a bar unaware that he was being filmed and made explicit remarks about Allardyce, who he replaced as Blackburn manager in December 2010.
The case was filed at the High Court in London on July 12. The full details of the High Court case have not been made public.