Arshavin made a good start to life in London but soon ran out of form and steam and spent the last few seasons on the fringes of the first team.
The winger made his name at Zenit, whom he helped to win the Europa League in 2008.
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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.