The Spanish shot-stopper is reported to be a target for the La Liga leaders after their current first-choice goalkeeper, Victor Valdes, announced his intention to leave Camp Nou.
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"David is very happy at Manchester United but of course he would like to return to Spain and if it's Barca it gets even better," she told a Catalan TV channel.
De Gea has endured a mixed campaign for the Red Devils this season, being regularly rotated by manager Sir Alex Ferguson.
The 22-year-old was also criticised for his display against Tottenham on January 20, when his weak punch allowed Spurs to score a late equaliser, while he similarly flapped at a Steven Gerrard shot to allow Daniel Sturridge to score at Old Trafford earlier in January.
Thibaut Courtois, on loan from Chelsea at Atletico Madrid, and Liverpool's Pepe Reina have also been linked with the soon-to-be-vacant No.1 position at Barcelona.