The 22-year-old struggled at times following his move from Atletico Madrid in 2011, but his form in the 2012-13 campaign saw him named in the Premier League team of the season.
However the Spaniard has been linked with a return to his homeland, and with Barcelona set to sell Victor Valdes this summer, De Gea has been mentioned as a possible target.
"I'm happy in Manchester," De Gea declared while on Under-21 duty for Spain.
"It has been a very good season, and the longer it goes, the better I'm there. I have a contract and hope to be at United for many years."
With the retirement of Sir Alex Ferguson, De Gea will work with a new manager, in the shape of David Moyes, and a new goalkeeping coach following the departure of Eric Steele when he does return to Old Trafford.
He said: "We are saddened by the departure of Ferguson, but in comes another great coach with a different style of play, so we will try to follow along the same lines and with the same tone.
"It's a shame that he went, he was great. But, now we have a new coach in David Moyes, who we still don't know. We're all waiting to get back there and see how it is with him."