The interactions between the solar wind and the neutral gas from Mars' moon Phobos and from the Martian exosphere are examined in order to check the feasibility of the energetic neutral atoms (ENA) remote sensing technique applied to Phobos' environment. Both solar wind and Mars exosphere models, as given in the literature, have been used. The density distribution of an outgassed neutral oxygen population located at Phobos' orbit has been simulated via Monte Carlo integration. Images and energy spectra of ENA, escaping through charge exchange processes, have been reconstructed applying a line of sight integration method. The performed simulation shows that the ENA signal originated from Phobos' environment is faint while observing far from Phobos location; anyway, it could be detected in some particular Mars-Phobos vantage point configurations. The possibility that the neutral oxygen outgassing rate might be estimated through ENA signal deconvolution is briefly discussed.