The 22-year-old has been mooted as a potential summer replacement for Barca 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."