The goalkeeper joined United from Atletico Madrid in the summer of 2011 and endured a mixed debut season as he struggled to establish himself as Sir Alex Ferguson's number one.
He again lost his place to Anders Lindegaard this season and that sparked rumours of a return to Spain, but the 22-year-old has no plans to leave Old Trafford.
"I'm very settled and feel like part of the furniture around the club," said De Gea in The Sun.
"I feel very much at home in the Premier League and, of course, with my team-mates here at the club. I'm enjoying life here and I feel I've settled well."
Parts of De Gea's goalkeeping have come under regular scrutiny during his time in England, but the Spaniard feels he is becoming a better player.
He added: "The biggest thing for me is that I've managed to work through some difficult times and those moments always make you stronger. It makes you a stronger person and a better player.
"I think I've improved right across the board, in all aspects of my game. I'm still only young and I feel as though I'm learning every day.
"I've hopefully got a long career ahead of me, so I want to soak up as much knowledge as I can while I'm young."
He continued: "I'm at a huge club now and there are big demands on you.
"As a goalkeeper, I'm well aware that any mistake can be magnified by the fans. But it's true that here at Manchester United there's added pressure.
"It's bigger right now than it was for me at Atletico Madrid and also for Spain Under-21s."