After jettisoning its Sample Return Capsule (SRC) containing regolith samples from the near-Earth asteroid (101955) Bennu to Earth in September 2023, the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) spacecraft will perform a divert maneuver and safely fly by Earth at an altitude of 250 km. SRC return and the divert maneuver officially mark the completion of the spacecraft’s primary mission; however, it will continue on in heliocentric orbit with a nearly fully-functional instrument suite and enough propellant for nearly 600 m/s Delta-V. The post-Earth flyby trajectory fortuitously enables an exciting extended mission opportunity: rendezvous with the near-Earth asteroid (99942) Apophis immediately following its historic Earth close approach in April 2029. In this paper, we detail the discovery, optimization, and analysis of the Apophis rendezvous trajectory for an extended OSIRIS-REx mission. We also present the technical approach for an alternate target search and corresponding results, assessing the alternate trajectories compared to the baseline Apophis rendezvous from a trajectory design standpoint.