The Daily Mail reports Allardyce has issued a claim against his old club Blackburn and their manager over comments his successor at Ewood Park is alleged to have made about him.
Disgruntled fans from The BRFC Action Group claimed responsibility for posting a video clip of him on the club's pre-season trip to Hong Kong last summer.
Speaking to supporters in a bar, Kean appeared to make unguarded comments about Allardyce in which he questions the integrity of the man who appointed him as first-team coach at Blackburn.
Allardyce instructed his lawyers to sue Kean for slander. He is taking legal action against Blackburn as well because Kean is an employee who was on club business at the time.