  We study the scalar field potential $V(\phi)$ in the scalar-tensor gravity
with self-consistent polytropic stellar configurations. Without choosing a
particular potential, we numerically derive the potential inside various
stellar objects. We restrict the potential to conform to general relativity or
to $f(R)$ gravity inside and require the solution to arrive at SdS vacuum at
the surface. The studied objects are required to obtain observationally valid
masses and radii corresponding to solar type stars, white dwarfs and neutron
stars. We find that the resulting scalar-tensor potential $V(\phi)$ for the
numerically derived polytrope that conforms to general relativity, in each
object class, is highly dependent on the matter configuration as well as on the
vacuum requirement at the boundary. As a result, every stellar configuration
arrives at a potential $V(\phi)$ that is not consistent with the other stellar
class potentials. Therefore, a general potential that conforms to all these
polytropic stellar classes could not be found.
