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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.