The Hawthorne-based company is negotiating a 10-year lease for an 18-acre parcel at the Port of Los Angeles.
SpaceX reportedly hopes to build commercial transportation vessels at the facility.
The company already leases about eight acres at the port for recovery of its Dragon capsules and first-stage boosters.
The company, owned by billionaire Elon Musk, also plans to design a deep-space rocket for missions to Mars and to transport passengers around the world in record time.