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The Russian club announced it on their social media channels, with reports suggesting the deal could be worth £11 million.
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The Croatia international had been linked with a move to AC Milan last summer after being shunted down the pecking order at Anfield to fourth-choice centre back - behind Virgil van Dijk, Joel Matip and Joe Gomez.
The 31-year-old signed for Liverpool from Southampton in 2014, for a transfer fee of £20 million.
ANOTHER LIVERPOOL LEGEND WHO LEAVES THE CLUB
“Another Liverpool legend who leaves the club, because he was absolutely a very, very important part of this team from the first day since I was in,” Klopp told Liverpoolfc.com.
He played super games and scored one of the most important goals of our history in the 4-3 against Borussia Dortmund; a really wonderful moment to share.
“He had so many good games. Yes, I think he will not like the Tottenham game when I took him off in the first half, but it is part of football and part of development – and he always came back.
“When he was fit, he was very, very, very often in the team. A great player and a great person."
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