The 26-year-old winger has been heavily linked with a move away from the Vicente Calderon when the transfer window reopens on July 1, but Turan has moved to quash speculation suggesting he could arrive in the Premier League.
"I feel happy and at peace here," the Turkish international told Spanish publication AS. "It has been a very successful season for the team."
Gunners boss Arsene Wenger has been credited with an interest in bringing Turan to the Emirates Stadium, while Chelsea owner Roman Abramovich is also believed to be monitoring the player's situation in Spain, ahead of a proposed bid to lure him to Stamford Bridge.
Turan has attracted attention from a number of clubs back in his homeland, but it's understood that he would rather see out his contract with Atletico Madrid, after Diego Simeone helped orchestrate the club's Champions League qualification for next season.
Galatasaray president Unai Aysal confirmed last week that the Turkish club would love to sign Turan if he became available, but admitted that they would be unable to rival Chelsea in terms of a big-money offer.
"Chelsea are involved with Arda and we won't be able to match what they are offering," Aysal was quoted by the Daily Mail.
"I met with the head of Atletico Madrid, he told me that there were three players the club definitely do not want to sell, one of them being Arda Turan."