Constructing set membership proof for private set Is it possible to construct a set membership proof to show $\delta \in \Psi$ where $\delta$ is publicly known and $\Psi$ should stay only known to the prover?

It seems rather impossible but I would like some confirmation.
Yes. $\:$ The verifier(s) need(s) to know a statistically binding commitment to $\Psi \hspace{-0.02 in}$.