The financing efforts follow new funding rounds by Elon Musk’s xAI and the market leader, OpenAI, which is now valued at $157 billion.

The San Francisco artificial intelligence start-up Anthropic is in talks to raise a new round of funding that could value the company at $60 billion, up from about $16 billion less than a year ago, according to two people with knowledge of the discussions.

Led by the venture capital firm Lightspeed Venture Partners, the new round could pump an additional $2 billion into the company, said the people, who spoke on the condition of anonymity. Since its founding in 2021, Anthropic has raised more than $11.3 billion from venture firms like Menlo Park Ventures and tech giants like Amazon, Google and Salesforce.

The talks come amid a new surge in funding for the industry’s most prominent A.I. start-ups. Last month, Elon Musk’s xAI raised $6 billion in a deal that valued the company at $35 billion to $45 billion. In October, OpenAI, the maker of the online chatbot ChatGPT, raised $6.6 billion at a $157 billion valuation.

OpenAI started the A.I. boom in late 2022 with the release of ChatGPT, setting off a funding surge that moved billions into a wide range of start-ups.

Enthusiasm among investors for A.I. companies cooled by the summer of 2024, as several high-profile start-ups were essentially folded into tech giants like Google and Amazon. But as companies like OpenAI and Anthropic have continued to improve their technology, interest among investors has regained steam.

(The New York Times has sued OpenAI and Microsoft, accusing them of copyright infringement of news content related to A.I. systems. OpenAI and Microsoft have denied those claims.)

Lightspeed Ventures declined to comment on Anthropic’s latest funding discussions. Details of the talks were reported earlier by The Wall Street Journal.

After founding Anthropic, Dario Amodei, the company’s chief executive, and his sister, Daniela Amodei, Anthropic’s president, positioned the company as a start-up that would build A.I. with guardrails.

Like several others on the company’s founding team, they had left OpenAI after disagreements with company leadership over how its technologies were being funded and released through Microsoft.

In a podcast interview in 2023, Mr. Amodei said there was a 10 to 25 percent chance that A.I. technology could destroy humanity. But in October, he struck a more optimistic tone, publishing a 14,000-word essay on the potential benefits of A.I. technologies.

“I think that most people are underestimating just how radical the upside of A.I. could be, just as I think most people are underestimating how bad the risks could be,” he wrote.

The next month, Anthropic raised $4 billion from Amazon, its largest investor, which has put a total of $8 billion into the start-up. Anthropic builds and operates its technologies using computer data centers owned by Amazon and Google.