The winger was a key member of the Atletico side who broke the domestic dominance of Real Madrid and Barcelona last season by claiming a first La Liga title since 1996 and also reached the final of the UEFA Champions League.
Atleti's success has already seen Diego Costa and Filipe Luis join Chelsea, while several other stars have been been tipped to depart Vicente Calderon.
Turan is the latest player to have been linked with a move away from the club, with Manchester United reportedly among his suitors.
But the Turkey international is not planning on leaving the Spanish capital.
"I'm with the best club in Spain," Turan said at a news conference ahead of Atleti's friendly with Galatasaray later on Wednesday. "I'm part of this system."
Meanwhile, coach Diego Simeone highlighted Turan as vital to Atletico in their quest for further honours this term.
"Arda is vital for us, due to his technical ability and his work ethic," Simeone commented. "He has grown a lot.
"He has natural talent and continues to be someone who makes a difference to the team."
Alexia Putellas: "We’re already the only club to have won the men’s and women’s Champions League, so the only thing even more historic to do than that would be to win it in the same season"
‘Trent has won everything he can for Liverpool, but of those who’ve left that we wanted to stay, who’s actually done better? I can only come up with one’: Reds legend highlights potential danger of Alexander-Arnold moving to Real Madrid
