We investigate the dynamical behavior of co-orbital asteroids of Venus, Earth, and Mars potentially affected by the von Zeipel-Lidov-Kozai (ZLK) mechanism. Semi-analytical models of the ZLK dynamics for NEOs in the terrestrial planet regions predict that at high eccentricities and inclinations, corresponding to i(max) =arccos[root 1-e(2) cos(inc)]>30(degrees), equilibrium points should appear at 90(degrees) and 270(degrees). At low eccentricities and inclinations in the vicinity of Earth and Venus, perturbations from these two planets are dominant, with two equilibrium points occurring at 0(degrees )and 180(degrees). Using numerical simulations performed with the SWIFT and REBOUND integrators, we classify the Kozai states of known co-orbitals and assess their long-term stability. Our results indicate that no current Venus co-orbital is a robust ZLK resonator, while several Earth co-orbitals and one Mars co-orbital (2017 XG62) exhibit libration around one of the four ZLK equilibrium points. Libration around the and equilibrium points protects asteroids from close encounters with their perturbing planet, Earth, enhancing long-term stability on timescales of similar or equal to 10(5) years. 2017 XG62 is the only known co-orbital asteroid of a terrestrial planet that is currently librating around the high-inclination equilibrium point. This configuration prevents this asteroid from experiencing close encounters with other terrestrial planets.