Turan's representative said last week that his client wanted a move to the Premier League and that three top English clubs had made bids for his services.
Reports in the Spanish press have claimed that the Turkey international is negotiating with Chelsea and Manchester United.
Turan tweeted: "The transfer rumours are not entirely correct.
"My agent is currently in touch with three or four clubs.
"I will update you all if a deal is made."
The 28-year-old has two years left on his contract with Atletico.
Outside of England, he has been strongly linked with Paris St Germain and Barcelona.
Turan, who joined Atletico in the summer of 2011 from Galatasaray for 12million euros (£8.5million), helped the Rojiblancos win the Copa del Rey three years ago and the Primera Division title during the 2013-14 campaign.
He scored two goals and set up four more in 32 Primera Division appearances to help Atletico finish third in the Primera Division this season.
Source : PA
Source: PA