The silver (Ag)-embedded lithium niobate (LiNbO3) composites are theoretically analyzed under the effective medium Maxwell-Garnett approximation to account on the optimal conditions through which such composites present negative epsilon conditions. The dielectric function of Ag nanoparticles (NPs) is described by Drude theory with an additional Lorentz oscillator term to take into account the interband electronic transitions which typically occur in noble metals. The LiNbO3 dielectric function is evaluated through the Sellmeier equations. Once the effective dielectric function (epsilon(eff)) is evaluated, we investigate the negative epsilon condition (epsilon'(eff) < 0) as a function of the frequency. The results showed that, for given volumen fraction values, the negative epsilon (NE) condition is satisfied for critical sizes of Ag NPs. This condition defines an interval of energies, called NE range. That NE range enlarges for increasing radius and becames narrower for decreasing volume fractions. Furthermore, the calculated Frohlich frequency is nearly close to the lower-energy limit of NE range. In addition, the calculated extinction spectra of the composite are analyzed in terms of the radius of Ag NPs.