The Montenegro international spent time with the Gunners after Arsene Wenger spotted him during a scouting mission in Belgrade.
He did not earn a deal, but the Partizan star remains on the club's radar.
Savic, 19, who lines up against Arsenal on Tuesday, said: "When the invitation came, it was a no-brainer.
"I spent 10 days in London, although it had been planned for me to stay only five days.
"Wenger is God. He has immense authority at the club and everyone listens to him. But from now on I am a Partizan player and I am fully focused on the club's ambitions."