  In the present work we study spherically symmetric gravitational collapse of
a homogeneous perfect fluid in the context of Generalized Rastall Theory (GRT).
In this modified version of the original {Rastall Gravity (RG)}, the coupling
parameter which is a representative of matter-curvature interaction is no
longer a constant parameter. Such a dynamic coupling may play the role of dark
energy which is responsible for the present accelerating expansion of the
Universe. Assuming then a linear equation of state (EoS) for the fluid
profiles, we seek for physically reasonable collapse scenarios in which the
spacetime singularity that occurs in general relativity (GR) is replaced by a
non-singular bounce. We therefore find that depending on model parameters, the
collapse process which starts from regular initial data, will halt at a minimum
value for the scale function and then turns into an expansion at a finite time.
We further find that there exists a minimum value for the initial radius of
collapsing object so that for radii smaller than this minimum radius, formation
of apparent horizon can be avoided and hence the bounce can be visible to the
observers within the Universe. We also compare our results to quantum corrected
collapse scenarios and find that the mutual interaction between matter and
geometry can play the role of quantum corrections to energy density.
