British media have repeatedly tipped the 20-year-old for a summer move to Old Trafford as a long-term replacement for Edwin van der Sar.
Last month De Gea's agent Hector Rincon said he had held talks with Manchester United over the keeper, adding most major European teams have shown interest in the Spaniard.
Asked about the reports linking him to a move to Manchester, De Gea said: "I have not signed anything, I am happy here. It is all a lie, I have a contract with Atletico until 2013 and the priority is to get the team into Europe.
"After the league is over, we will see. Until the end of the season nothing will be decided.
"There is nothing to report now, I am calm, although later on we will see. If Atletico wants me and fights for me, it will be hard for me to leave."
Atletico Madrid are in eighth place in the league standings, 42 points behind defending champions and leaders Barcelona.