  We propose a scheme of searches for the $Z'$ gauge boson as a virtual state
in scattering processes at the Tevatron taking into account model-independent
relations between the $Z'$ couplings to fermions. We integrate the Drell-Yan
process cross setion to construct two-parametric observables, which are
suitable for $Z'$ searches in the $p\bar{p} \to l^+ l^-$ process. The
observables allow to constrain the $Z'$ vector and axial-vector couplings to SM
fermions in a general parameterization with non-universal $Z'$ interactions
with fermion generations. Also a one-parametric observable for searching for
the popular leptophobic $Z'$ boson is proposed.
