Space gravity measurements have been mainly used to study the temporal mass variations at the Earth’s surface and within the mantle. Nevertheless, mass variations due to the Earth’s core might be observable in the gravity field variations as measured by GRACE(-FO) satellites. Earth’s core dynamical processes inferred from geomagnetic field measurements are characterized by large-scale patterns associated with low spherical harmonic degrees of the potential fields. To study these processes, the use of large spatial and inter-annual temporal filters is needed. To access gravity variations related to the Earth’s core, surface effects must be corrected, including hydrological, oceanic or atmospheric loading (Newtonian attraction and mass redistribution). However, these corrections for surface processes add errors to the estimates of the residual gravity field variations enclosing deep Earth’s signals. As our goal is to evaluate the possibility to detect signals of core origin embedded in the residual gravity field variations, a quantification of the uncertainty associated with gravity field products and geophysical models used to minimise the surface process signatures is necessary. Here, we estimate the dispersion for GRACE solutions as about 0.34 cm of Equivalent Water Height (EWH) or 20% of the total signal. Uncertainty for hydrological models is as large as 0.89 to 2.10 cm of EWH. We provide estimates of Earth’s core signals whose amplitudes are compared with GRACE gravity field residuals and uncertainties. The results presented here underline how challenging is to get new information about the dynamics of the Earth’s core via high-resolution, high-accuracy gravity data