Context: The dynamics of the solar core cannot be properly constrained through the analysis of acoustic oscillation modes. Gravity modes (g modes) are necessary to understand the structure and dynamics of the deepest layers of the Sun. Through recent progress on the observation of these modes - both individually and collectively - new information is available to contribute to inferring the rotation profile inside the nuclear burning core. Aims: We aim to see the sensitivity of gravity modes to the rotation of the solar core. We analyze the influence of adding the splitting of one and several g modes to the data sets used in helioseismic numerical inversions. We look for constraints on the uncertainties required in the observations to improve the derived core rotation profile. Methods: We compute three artificial sets of splittings derived for three rotation profiles: a rigid profile taken as a reference; a step-like profile and a smoother profile with higher rates in the core. We compute inversions based on regularized least-squares methodology (RLS) for both artificial data with real error bars and real data. Several sets of data are used: first, we invert only acoustic modes (p modes), then we add one and several g modes to which different values of observational uncertainties (75 and 7.5 nHz) are attributed. For the real data, we include g-mode candidate, ℓ=2, n=-3 with several splittings and associated uncertainties. Results: We show that the introduction of one g mode in artificial data improves the rate in the solar core and gives an idea of the tendency of the rotation profile. The addition of more g modes lends greater accuracy to the inversions and stabilizes them. The inversion of real data with the g-mode candidate gives a rotation profile that remains unchanged down to 0.2 R&sun;, whatever value of splitting we attribute to the g mode.