If expansion is growing separation of comoving and force free worldlines and contraction is shrinking separation between them then yes, in the close field where matter collapses you can describe this as space falling into the center of mass if you use the Raindrop analogy as you see in the Gullstrand Painlevé equivalent form of the FLRW metric in Proper Distance coordinates where the radial space flow velocity $\rm v=g_{tr}=-c\sqrt{r_s/r}$ is replaced by $\rm v=g_{tr}=+H r$, so in that sense in the close field where the sign is negative space can be described as contracting while in the far field where the sign becomes positive as expanding. For a single mass in an otherwise dark energy dominated universe the distance where the sign changes would be at $\rm r=\sqrt[3]{G M/H^2}$.

If expansion is growing separation of comoving and force free worldlines and contraction is shrinking separation between them then yes, in the close field where matter collapses you can describe this as space falling into the center of mass if you use the Raindrop analogy as you see in the Gullstrand Painlevé equivalent form of the FLRW metric in Proper Distance coordinates where the radial space flow velocity $\rm v=g_{tr}=-c\sqrt{r_s/r}$ is replaced by $\rm v=g_{tr}=+H r$, so in that sense in the close field where the sign is negative, space can be described as contracting while in the far field where the sign becomes positive as expanding. For a single mass in an otherwise dark energy dominated universe the distance where the sign changes would be at $\rm r=\sqrt[3]{G M/H^2}$.