The controversial Green Brigade said they would not be attending the club's Champions League play-off match with Maribor on Tuesday.
The leaders said they had "exhausted pretty much all avenues" in trying to find a solution.
Last season Celtic disbanded the Green Brigade section at Parkhead after seats were damaged at Fir Park, Motherwell, just above where a Green Brigade banner was displayed.
The Green Brigade said: "The situation looks bleak.
"We have exhausted pretty much all avenues in attempting to secure a permanent, club-sanctioned section.
"It is becoming increasingly clear some at the club must not be interested in the prospect of us returning to Celtic Park."