The existence of an observed meteor shower associated with some Near-Earth Asteroid (NEA) is one of the few useful criteria that can be used to indicate that such an object could be a candidate for being regarded as an extinct or dormant cometary nucleus. In order to identify possible new NEA-meteor showers associations, the secular variations of the orbital elements of the NEA 2000 PG3, with comet-like albedo (0.02), and moving on a comet-like orbit, was investigated under the gravitational action of the Sun and six planets (Mercury to Saturn) over one cycle of variation of the argument of perihelion. The theoretical geocentric radiants and velocities of four possible meteor showers associated with this object are determined. Using published data, the theoretically predicted showers were identified with the night-time September Northern and Southern δ-Piscids fireball showers and several fireballs, and with the day-time meteor associations γ-Arietids and α-Piscids. The character of the orbit and low albedo of 2000 PG3, and the existence of observed meteor showers associated with 2000 PG3 provide evidence supporting the conjecture that this object may be of cometary nature.