The Spaniard has been exceptional in recent seasons and believes the history at Old Trafford makes a move to the club appealing.
De Gea has been linked with a move to Real Madrid in recent seasons but has so far stayed put at United.
The Red Devils signed the 26-year-old from Atletico Madrid back in 2011.
De Gea explained: “I think for any player, any young kid, it is a dream to come and play for Manchester United.
“Probably because of the history of the club and the players that have come through this particular club in the past, making it one of the best in the world.
“As I said, any child will always grow up wanting to play for this team”
Man Utd goalkeeper David De Gea
“As I said, any child will always grow up wanting to play for this team.”
De Gea also believes he in in top form for United but will continue to work hard to get even better.
He added: “Yes, it’s obviously lovely to hear that, if people are putting you up there as one of the best goalkeepers in the world.
“I’m feeling very confident at the moment but I’m training hard to continue to play at this high level, and I have been playing at this high level for quite a long time.
“I will train hard to get even better and improve even more.”
De Gea has started the season well for Jose Mourinho’s side, keeping seven clean sheets in 10 matches.
Next up for United is a clash with arch rivals Liverpool at Anfield in the Premier League after the international break.