UPDATE: Elon Musk has dispelled this rumor. Instead, he suggests that the current airport should add another runway. See Musk's tweet below:
Tesla CEO Elon Musk reportedly wants to build an airport near Bastrop, an eastern suburb of Austin. According to a report by local outlet Austonia, Musk intends to use the airport not just for himself but also for employees of his numerous companies. Musk is a big fan of the Texan city, having relocated several of his firms' HQs from Palo Alto and Los Angeles to Austin.
Building a new airport would not be an easy task for Musk. EPA and FAA approvals are required, with environmental and air traffic impacts having to be analyzed. That said, Musk has overcome numerous planning hurdles in the past, most recently with Giga Berlin.
Per a 2019 report from The Washington Post, Musk flies around 150,000 miles a year. This equates to over 6 times the earth's circumference. He currently owns four private jets - a $70 million Gulfstream G650ER, two $61.5 million Gulfstream G550s, and a $26 million Dassault Falcon 900B. A teenager who tracks all of Musk's flights and tweets about them, Jack Sweeney, recently refused a $5,000 offer from Elon to stop. He did say he would consider shutting down his account in exchange for a Tesla Model 3, however.
The exact size of the airport is unknown, although sources state conceptual plans have been confirmed. For reference, Austin Executive Airport (used primarily for mid-sized private jets) has over 130,000 square feet of hanger space and a 6,025-foot runway.
It's important to note so far none of this has been confirmed by Musk or any of his reps. Therefore, the above reports should be taken as unconfirmed for now.