The company behind the Claude chatbot said in a regulatory filing on Tuesday it would sell 825 million shares priced between $US70 ($A101) and $US78 ($A113) per share.
That would give Anthropic the ability to raise more than $US61 billion ($A88 billion), if the initial public offering (IPO) is priced at the midpoint.
The San Francisco-based company is expected to make its Wall Street debut this month.
Anthropic could wind up being the biggest IPO ever, possibly eclipsing the record $US86 billion ($A125 billion) raised by SpaceX in its IPO in June.
An Anthropic IPO would also put the company ahead of OpenAI in going public, setting the stage for a pair of blockbuster stock debuts by rival AI developers.
The IPO could give Anthropic enormous resources to accelerate its expansion and potentially add billions of dollars to the fortunes of chief executive Dario Amodei and his sister and co-founder, Daniela.
A regulatory filing last month showed Anthropic's revenue is growing rapidly, reaching more than $US16 billion ($A23 billion) in the first half of the year — 14 times its revenue from the same period last year.
But like many other tech companies going public, the company is yet to turn a profit.
Formed in 2021 by former OpenAI leaders, Anthropic is locked in a fight for dominance with that company.
But both companies have plenty of other competitors including Google, newer startups in the US and China, and SpaceX, which has an AI business.
Anthropic, OpenAI and SpaceX's AI division have all been losing more money than they make because of the huge costs of resources in building AI, fuelling concerns of a bubble.
Amodei cautioned in September the AI industry should slow its fast-moving development to give safety measures time to catch up.
Without such a slowdown, AI could be capable of letting loose a swarm of agents that could take over the entire internet within six to 12 months, Amodei warned.
He offered a plan in a post on his website to increase checks on the industry, saying Anthropic was already undertaking part of this on its own.
As for other steps, he said that would require coordination across the industry and with governments around the world, including authoritarian ones.
Reuters reported on Monday that Anthropic briefly circulated details of its IPO filing in emails to bankers that were then retracted as inaccurate.
