But he added that such a project would need the support of Puerto Rico – something the governor appears to be open to.
It is also understood that Tesla has already sent a number of battery systems to Puerto Rico to store energy from the island’s existing solar panels to help offset the energy shortage.
The latest conversation is reminiscent of the bet started on Twitter between Mr Musk and an Australian software entrepreneur which led to plans for the world’s largest battery storage project in South Australia.
That battery installation – which Tesla guaranteed could be working “100 days from contract signature” – was declared half-built within days of the start of construction.
The Puerto Rican governor also used the exact same language – “let’s talk” – as South Australia Senator Sarah Hanson-Young used before the project became a reality.
Puerto Rican residents with solar panels are among the few with a stable electricity supply.
One flower grower, Hector Santiago, invested $300,000 (£230,000) in solar panels six years ago, Reuters reported this week.
“Everybody told me I was crazy because it was so expensive. Now I have power and they don’t,” he told the agency.
It is understood that Tesla has already sent a number of battery systems to Puerto Rico to store energy from the island’s existing solar panels to help offset the energy shortage.
Mr Musk has been largely successful in his renewable ventures.
Alongside his successful Tesla motors company and solar projects, he is also the founder of SpaceX, which has developed reusable rockets for space flight.
Last week, he unveiled plans for a city to city rocket transport system, which could fly people from London to New York in less than half an hour, and for a manned Mars mission by 2024.