Musk's bid is likely to ratchet up longstanding tensions with OpenAI CEO Sam Altman over the future of the ChatGPT maker at the heart of a boom in generative AI technology.
Altman promptly posted on X: "no thank you but we will buy twitter for $9.74 billion if you want."
Musk co-founded OpenAI with Altman in 2015 as a nonprofit, but left before the company took off. He founded the competing AI startup xAI in 2023.
Musk, the CEO of Tesla and owner of tech and social media company X, is a close ally of US President Donald Trump. He spent more than a quarter of a billion dollars to help elect Trump, and leads the Department of Government Efficiency, a new arm of the White House tasked with radically shrinking the federal bureaucracy.
Musk recently criticised a $US500 billion OpenAI-led project announced by Trump at the White House.
OpenAI is now trying to transition into a for-profit from a nonprofit entity, which it says is required to secure the capital needed for developing the best AI models.
Musk sued Altman and others in August last year, claiming they violated contract provisions by putting profit ahead of the public good in the push to advance AI. In November, he asked a US district judge for a preliminary injunction blocking OpenAI from converting to a for-profit structure.
Musk's lawsuit against OpenAI and Altman says the founders originally approached him to fund a nonprofit focused on developing AI to benefit humanity, but that it was now focused on making money.
"It's time for OpenAI to return to the open-source, safety-focused force for good it once was," Musk said in a statement. "We will make sure that happens."
Altman told staff in a message that the company's board of directors intends to make clear it has no interest in Musk's "supposed bid", according to a report by The Information on Monday.
Musk and OpenAI backer Microsoft did not immediately respond to requests for comment.
The consortium led by Musk includes his AI startup xAI, Baron Capital Group, Emanuel Capital and others.
xAI could merge with OpenAI following a deal, according to the Wall Street Journal, which first reported Musk's offer earlier on Monday. xAI recently raised $US6 billion from investors at a valuation of $US40 billion, sources have told Reuters.
OpenAI was valued at $US157 billion in its last funding round, cementing its status as one of the most valuable private companies in the world. SoftBank Group is in talks to lead a funding round of up to $US40 billion in OpenAI at a valuation of $US300 billion, including the new funds, Reuters reported in January.