The Red Devils have managed to fend off interest from the La Liga giants in their number one over the past three or four seasons.
De Gea came close to a move to The Bernabeu in a £25m deal in the 2015 summer transfer window before the deal fell through on Spain’s deadline day.
The 27-year-old has been consistently one of Manchester United’s best players since Sir Alex Ferguson’s retirement in 2013.
Real Madrid are rumoured to be in the market to sign a new shot stopper in the summer with De Gea and his Chelsea rival Thibaut Courtois at the top of their list.
Former Liverpool FC and Manchester City striker Bellamy believes there is a sense of inevitability that De Gea will move to Old Trafford.
“He is the real deal and I have always felt that Real Madrid have been looking for him to be their number one for a number of years,” Bellamy told The Debate on Sky Sports on Wednesday night.
“And it is just a matter of time before they get him. His footwork is brilliant, he anticipates as well, he can read forwards and if you watch, he makes a lot of his saves with his feet.
“He is incredible. He asks the forward so many questions when you are gunning down on him and he is a real top goalkeeper.”
De Gea has won the Premier League title, the FA Cup, the Europa League and the League Cup during a seven-season spell at Old Trafford.
Manchester United will take on La Liga side Sevilla in the Champions League round of 16 later this month as De Gea looks to win the competition for the first time.
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