The 22-year-old is reportedly being considered by the Spanish giant as it starts its search for Victor Valdes' replacement, but he insists he is happy in England.
The 22-year-old Spaniard has overcome some inconsistent form at the start of his Old Trafford career with Barcelona reportedly keen on him after it was made clear that Victor Valdes will leave the club at the end of next season. However, De Gea has reiterated his desire to stay in Manchester for the time being.
"I know things have been said and written but I have a contract. I'm very well in Manchester," De Gea told reporters. "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."
The current Spain Under-21's captain has highlighted the influence Sir Alex Ferguson had on his improved play, calling the manager a 'father' figure at the club.
"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," De Gea added. "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 says that without Nani's red card in the Champions League tie against Real Madrid, Manchester United would be in the quarterfinals of the cup.
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 quarterfinals."