The interaction between nanogels is a central question in the field of soft matter which has been scarcely studied. In fact, effective potentials for nanogels are less advanced than for other colloidal particles. The soft-sphere potential and the Hertz potential are two theoretical formalisms used until now by some authors to quantify forces between nano- and microgels. Accordingly, in this work we have performed explicit coarse grained Monte Carlo simulations to find out if these models can capture the interactions between overlapping neutral nanogels. To this end, pairs of nanogels with different number of monomers per chain have been simulated, and the corresponding effective interaction potentials have been calculated as a function of the distance between their respective centers of mass. Then, our simulation results have been used to analyze the functional form of the soft-sphere and Hertz potentials. Both are too simple to describe nanogel interactions when these nanoparticles overlap to a significant extent and can only be employed as a first approach in the regime of small deformations. The simulations performed here also reveal that the interaction can be described within the Hertz model in terms of a bit greater diameter than the geometrical one. In addition, simulations together with theoretical calculations have also performed to deepen into the interaction strength parameter included in the Hertz model. This parameter is a function of the nominal particle diameter as well as Young's modulus and Poisson's ratios, and it might exhibit a nonmonotonic behavior that depends on the number of monomers per chain in the nanogels. The results presented here are also analyzed modifying the exponent of the classical Hertz model.