  We study the inclusive near-threshold production of $\eta^\prime$ mesons in
$\pi^-$ meson-nucleus reactions on the basis of the first-collision model
relying on the nuclear spectral function and including incoherent processes of
$\eta^\prime$ production in $\pi^-$ meson--proton collisions. The model
accounts for the absorption of initial $\pi^-$ and final $\eta^\prime$ mesons,
the binding of intranuclear protons and their Fermi motion, as well as the
effect of the scalar $\eta^\prime$--nucleus potential (or the in-medium shift
of the $\eta^\prime$ meson mass) on these processes. We calculate the
differential and total cross sections for $\eta^\prime$ production off carbon
and tungsten nuclei at laboratory angles of 0$^{\circ}$--10$^{\circ}$ and
10$^{\circ}$--45$^{\circ}$ by $\pi^-$ mesons with momentum of 1.7 GeV/c, which
is close to the threshold momentum for $\eta^\prime$ creation on a free target
proton at rest. We show that the calculated $\eta^\prime$ production cross
sections are larger than those, studied earlier in the $\eta^\prime$
photoproduction reactions, by about two orders of magnitude. We also
demonstrate that the high absolute values of the present differential and total
$\eta^\prime$ production cross sections in the momentum ranges of 0.2--0.3
GeV/c and 0.1--0.6 GeV/c, respectively, possess a high sensitivity to changes
in the in-medium shift of the $\eta^\prime$ mass. This offers the possibility
of evaluating the above shift at these momenta from the respective data, which
could be taken in future experiments at the GSI pion beam facility or at
J-PARC.
