Allegri looks increasingly likely to depart the San Siro after an appalling start to the season.
Rijkaard, who coached Barcelona to Champions League success in 2006, could step straight into his shoes, reports 7Gold.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.