The Serie A side announced on Sunday that the 24-year-old centre-back was??on the verge of moving to another club.
And he now looks poised to become Atletico’s latest signing after telling Marca at Madrid airport that he is “very happy” to be joining “a great club”.
“(Diego)??Simeone is the best coach in football and I am looking forward to meeting him,” he said.
“I hope to talk soon with him to see what is expected of me, I am eager to join the group and am very happy. I am going to have a medical and then join up with the squad.”
Savic, who is under contract with Fiorentina until June 2019, joined the Serie A side three years ago from Manchester City and made 28 league starts in the 2014-15 season.
The Spanish press report that, as part of the deal that will bring Savic to the Vicente Calderon, Atletico midfielder Mario Suarez will move the opposite way.
Suarez made 11 league starts for Atletico in the recently concluded campaign and is willing to leave the Rojiblancos in search of more playing time.