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The Reds saw off competition from Arsenal for the Turkey international, who helped Madrid win the Primera Division title last season.
A statement on www.liverpoolfc.com read: "The 23-year-old will now undergo a medical on Merseyside."
Sahin will be the fourth new arrival at Anfield following Joe Allen, Fabio Borini and Oussama Assaidi.
The midfielder joined Madrid last summer after catching the eye during a successful spell with Borussia Dortmund, with whom he won the Bundesliga title in 2010/11.
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Sahin has also won 31 caps with Turkey, scoring his first national goal aged just 17 against Germany in 2005.
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