Arda has a contract with Atletico until June 2017 but his agent, Ahmet Bulut, has been quoted as saying in recent days the 28-year-old is keen to play in the English Premier League.
Chelsea or Manchester United are seen as likely destinations, with Ligue 1 champions Paris St Germain and Italian side AC Milan also in the hunt, according to reports.
"The transfer rumours are not entirely correct," Arda said on his Twitter feed on Sunday.
"My agent is currently in touch with 3-4 clubs," he added. "I will update you all if a deal is made."
Arda, who has a market value of 35 million euros ($39.1 million) according to website Transfermarkt.com, has become a hugely popular figure with the Atletico fans in his four seasons in the Spanish capital since joining from Galatasaray.
He was a key figure in their charge to a first La Liga title in 18 years and their run to the Champions League final in 2013-14.
Atletico are poised to sign Jackson Martinez from Porto, the Colombia striker said on Friday, and have also agreed to buy Argentine forward Luciano Vietto from Villarreal, Villarreal president Fernando Roig said last week.
(Reporting by Iain Rogers, editing by Toby Davis)
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