De Gea has come under fire for a string of errors this season.
But the Spain Under-21 international insists that he is keen to emulate the success of Peter Schmeichel and Edwin van der Sar at Old Trafford.
He said: “I have every intention of spending many years here at Manchester United.
“I want to become a great United keeper and I want to earn and deserve the respect I hope to get.
“I want to help United make history.”
De Gea said of his current run of poor form: “Let’s face it, all keepers make mistakes once in a while and none of us like it when we do.
“It’s well known that the style of play in England is rather more physical and as a goalkeeper you’ve got to be right on it.
“You’ve got to be attentive all through the match.
“The players coming at you can shoot from any angle, and they can shoot from distance.
“There’s also a lot of crosses from the sides, a lot of high balls and aerial play.
“So, you’ve got to get in there and block and stop shots being taken.”
