We present magnetization and muon-spin spectroscopy measurements of Néel skyrmion-host GaV4S8 under the application of hydrostatic pressures up to P = 2.29 GPa. Our results suggest that the magnetic phase diagram is altered with pressure via a reduction in the crossover temperature from the cycloidal (C) to ferromagnetic-like state with increasing P , such that, by 2.29 GPa, the C state appears to persist down to the lowest measured temperatures. With the aid of micromagnetic simulations, we propose that the driving mechanism behind this change is a reduction in the magnetic anisotropy of the system, and suggest that this could lead to an increase in stability of the skyrmion lattice.