The veteran is facing a backlash from Hajduk Split fans after new coach Rino Gattuso revealed Perisic had told him he wanted to leave.
Perisic joined Hajduk Split on-loan from Spurs in January before signing permanently in June.
But he has now been frozen out of the squad by Gattuso, with the Italian explaining: "20 days ago he came to my office and said that he would like to leave Hajduk.
"If someone doesn't want to stay then I have to respect the rest of the team, and in the locker room there are rules that must be respected. I gave him the opportunity to play, 20 minutes, 35 minutes, 65 minutes. If a player expresses the desire to leave, it can lead to wrong thoughts.
"This is not a closed story because he is still here."
Perisic has now disabled comments on his Instagram account as he battles a backlash from unhappy fans. A move away is now likely for the former Inter Milan star.