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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.