With Iker Casillas being tipped to leave the Bernebeu next summer, Real Madrid are hunting for a new goalkeeper, and De Gea is currently at the top of their list to replace the Spain captain.
Although the 24-year-old had earlier dismissed speculations of him moving to Real Madrid, insisting he was happy at Manchester United, recent reports have indicated that the Spaniard will be leaving Old Trafford if the Red Devils fail to qualify for the Champions League for a second successive season.
As a result, Real Madrid have reportedly stepped up their interest in De Gea, with there being claims of the Los Blancos already making contact with the Spaniard over a potential summer move, according to the Metro.
Manchester United, on the other hand, are reportedly targeting free agent Valdes if De Gea does move to Madrid next summer.
The 32-year-old goalkeeper, who left Barcelona at the end of last season after his contract expired, has been training with the Red Devils to regain his fitness following a lengthy spell on the sidelines due to an anterior cruciate ligament injury he sustained while playing for the Catalan club in March.
Although Manchester United midfielder recently Juan Mata revealed that Valdes has not made up his mind on where he will play next, the Metro claim that the Spaniard will be joining the Red Devils if De Gea moves to Real Madrid next summer.
Meanwhile, Marouane Fellaini wants to stay clear of injuries so that he can be consistent at United this season.
Last season, Fellaini was plagued by numerous injuries and this resulted in him failing to impress in his debut campaign at Old Trafford.
However, this season, the former Everton midfielder has found some form after an early-season injury.
"It's difficult when you come in and then you stop for a few weeks or months because of injury, and you have to wait again," he told Manchester United's official website. "I want to stay fit now – very fit. I feel I can be dangerous if I stay fit."