Elon Musk’s artificial intelligence start-up, xAI, is in talks to raise new financing that could value it at as much as $40 billion, up from $24 billion five months ago, three people with knowledge of the discussions said.

The talks are in the early stages, two of the people said, and the start-up’s valuation could fall into the mid-$30 billion range if the talks continue. Investors have discussed putting another $5 billion into the company, two of the people said, a figure that could also change as the discussions progress.

The talks follow a huge fund-raising effort by OpenAI, the San Francisco start-up that makes ChatGPT, which said this month that it had closed on financing that valued it at a whopping $157 billion. OpenAI launched the A.I. boom in late 2022 with ChatGPT’s release, spurring a funding surge for other A.I. companies, including xAI.

Enthusiasm among investors for A.I. companies has cooled in recent months, as several high-profile start-ups have essentially been folded into tech giants like Google and Amazon. But xAI and OpenAI are among the few that continue to seek billions in funding to build the leading A.I. technologies.

In May, xAI raised $6 billion, while rival Anthropic raised hundreds of millions of dollars in 2023 and in recent months has floated the idea of more funding with investors.

Mr. Musk did not respond to a request for comment about xAI. Details of the talks were earlier reported by The Wall Street Journal and The Information.