  An LCK manifold with potential is a compact quotient M of a Kahler manifold X
equipped with a positive plurisubharmonic function f, such that the monodromy
group acts on $X$ by holomorphic homotheties and maps f to a function
proportional to f. It is known that M admits an LCK potential if and only if it
can be holomorphically embedded to a Hopf manifold. We prove that any
non-Vaisman LCK manifold with potential contains a complex surface with
normalization biholomorphic to a Hopf surface H. Moreover, H can be chosen
non-diagonal, hence, also not admitting a Vaisman structure.
