Spanish newspaper El Mundo Deportivo claims that De Gea wants the opportunity to speak to Barcelona regarding a move as the La Liga giants prepare for life after Victor Valdes.
The current Barca number one will leave the club at the end of the season as his contract expires. Several Premier League stoppers have been mentioned as possible replacements, including Chelsea keeper Thibaut Courtois.
But the report claims De Gea has instructed his agent, Jorge Mendes, to listen to offers from Barca if they firm up their interest.
As is often the case when it comes to transfer speculation though, a rival paper has a slightly different take.
Because The Daily Mail reports De Gea is actually on the cusp of agreeing a new United contract, having settled down at Old Trafford and established himself as number one.
After an unconvincing start to his United career following his move from Atletico Madrid, the Spaniard has won the trust of the Old Trafford hierarchy, and he was exceptional for large parts of last season as United won the Premier League.
The Daily Mail report states that De Gea is in line for a £15,000-a-week salary bump, taking his weekly wage up to the £75,000-a-week.
Barcelona will need to replace Valdes before the start of next season, and the El Mundo Deportivo report goes on to claim that the Nou Camp bosses have been impressed by De Gea's development in the Premier League.
And they believe he would be keen to return to Spain if given the opportunity.