In this work, we aim to study numerically the emission decay rate of a hybrid system combining a quantum emitter (QE) and an epsilon-near-zero (ENZ) spherical nanoparticle (SNP). Inspired by the peculiar behavior of ENZ materials and their high potential in developing unusual abilities in controlling the emission properties of QE. More specifically the control of fluorescence inhibition, or the amplification of the lifetime of the excited state. This can naturally find applications in quantum information storage for optical quantum memories based on light-atom interaction which naturally benefit from storage time control. We demonstrate that the key process in limiting fluorescence inhibition is the competition between inhibition of fluorescence from the radiative processes and energy dissipation due to the non-radiative channels. Furthermore, we illustrate that this balance can be shifted to optimize inhibition as function of the QE position. The optimization happens via SNP size control, material composition, and λENZ of the SNP. This detailed study introduces and paves the way for new research directions on the manipulation and optimization of QE properties in the vicinity of ENZ materials.