Valdes' future with the Catalans remains unclear after contract negotiations with the player stalled recently, and de Gea is understood to be the top name on a shortlist to replace him.
Barcelona wanted de Gea years ago and came close to signing him back when he was a youth team player at Atletico Madrid, only to be deterred by the £500,000 asking price.
Instead, the Spaniard ended up joining the Red Devils in the summer of 2011 for £17 million and was viewed by manager Sir Alex Ferguson as a replacement for the recently retired Edwin van der Sar.
But de Gea hasn't found life at Old Trafford easy and has been regularly competing with Dane Anders Lindegaard for the number one jersey. Though the Spaniard is now enjoying some consistency as Ferguson's preferred goalkeeper, he has only kept three clean sheets all season and was at fault for Liverpool's goal at Old Trafford at the weekend.
However, Barca scouts have been watching his recent performances and have apparently presented a glowing report about his ability.
He is thought to be one of five names shortlisted by Barcelonas director of football Andoni Zubizarretta.
The others are Romas Maarten Stekelenburg, Vicente Guaita of Valencia, Borussia Moenchengladbach keeper Marc Ter Stegen and Bernd Leno of Bayer Leverkusen.