The Dons have sold out three stands at Celtic Park and asked if extra tickets could be released ahead of Sunday's clash against Inverness.
But the only section available is the upper tier of the Lisbon Lions Stand, above the Inverness support, and that has been ruled out.
A spokesman for the Scottish Professional Football League said: "We have spoken to the police and safety officer about releasing seats in the Lisbon Lions Upper, however that has been declined."
Inverness are believed to be edging towards selling their initial 7,500 allocation.
Caley Thistle had complained about the SPFL's draft stadium plan, which would have allowed more scope for providing extra batches of tickets in the 60,000-capacity arena, but would have seen their support spread across the Lisbon Lions and main stands.