The 22-year-old is enjoying his second season at United following a 2011 move from Atletico Madrid and has played a key role in the club's relentless pursuit of the title in recent weeks.
He has been mooted as a potential summer replacement for Barcelona keeper Victor Valdes, but De Gea says he is in no rush to leave Old Trafford.
"I know things have been said and written but I have a contract," De Gea is quoted in The Sun. "I'm very well in Manchester.
"It is not just my name that appears. At Barca, Valdes is still the keeper and Madrid is my city, one day I'd like to return.
"But now I hope to stay in Manchester for a long time and win a lot of titles."
De Gea also praised the man-management skills of Sir Alex Ferguson after the United boss helped him to deal with the criticism which has come his way.
He added: "Sir Alex is more than a manager. He controls everything in the team. He's a father for all those who come to the club. For that he is the best.
"A footballer has to get used to good and bad words.
"At times things are said that don't make a lot of sense and it is part of the job to know how to live with that. The best thing is to know who you are always."
Meanwhile, De Gea believes that United would have reached the quarter-finals of the UEFA Champions League if Nani had not been controversially sent off in the second leg against Real Madrid.
He continued: "Sir Alex has a lot of character and on that day he was very angry, although deep down what he felt more was pride for his team.
"We were superior to Madrid and deserved more but there were situations - unfair decisions - and we were knocked out.
"Football is like that and in that type of game details leave you knocked out. The expulsion of Nani marked the game and the tie. Without that red card it would be Manchester United in the quarter-finals."