Mundo Deportivo report that the Spanish giants are keen to bring in a long term replacement for Victor Valdes.
De Gea, whose United future is uncertain, could be brought to the Camp Nou to fill that role.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.