Spanish newspaper Marca reports that the Spanish giants are ready to send the midfielder out on loan.
Sahin has failed to make the expected impact at Real Madrid since joining the club from Borussia Dortmund last summer.
The 23-year-old has been linked with the likes of Arsenal, Tottenham, Liverpool, Manchester United and Besiktas.
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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.