Sahin had been on loan at Liverpool but barely featured for Brendan Rodgers’ side.
He is still owned by Real Madrid, who appear reluctant to allow the player to make a permanent switch away from the Bernabeu.
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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.