The Boring Company's machine for digging a tunnel under Los Angeles. Screenshot Elon Musk said he is making progress on his ambitious tunneling plans for Los Angeles.

The Tesla and SpaceX CEO said on Twitter Sunday that he has had "promising conversations" with Eric Garcetti, the mayor of Los Angeles, about building an underground network of tunnels under Interstate 105 in LA.

"Promising conversations with Mayor of LA regarding tunnel network that would carry cars, bikes, and pedestrians. Permits harder than technology," Musk said.

Musk officially launched his tunnel company, aptly named The Boring Company, in April. The company's ultimate goal is to build as many as 30 layers of tunnels underground that can transport cars on an electric skate and even accommodate a Hyperloop.

The Boring Company is building its own tunneling machine that Musk has said is more powerful than other machines in use today by "a factor of four or five."

Los Angeles is considering the addition of an express train that would travel between Los Angeles International airport and Union Station, a main railway stop in the city. Garcetti said in an interview with ABC7 that he is considering using Musk's tunnel to support the rail connection.

"I would love to see, maybe even with the new tunnel technology that people like Elon Musk is looking at, whether we can have a quick and direct route from LAX to Union Station," Garcetti said.

The Boring Company, led by SpaceX engineer Steve Davis, is currently building a demo tunnel in the SpaceX parking lot, which is a five-minute drive from LAX. But the company will need to secure permits to extend the tunnel beyond the SpaceX property line.