The Cambridge-based company aimed to raise $10 billion (£8 billion).
In March, the company dealt a blow to the UK by announcing that it had no intention of listing its shares in London.
Arm was bought by Japanese firm SoftBank in 2016 in a deal worth £23.4bn. At the time, Arm was listed in both London and New York.
The company creates the technology that powers processors, also known as chips, in various devices, including smartphones and game consoles.
Its designs are used by chip makers such as Taiwan Semiconductor Manufacturing Company and household brands such as Apple and Samsung to build their processors.
SoftBank said it had “submitted a draft registration statement confidentially” to the US Securities and Exchange Commission (SEC) for listing.
The announcement did not disclose how much it planned to raise or when the shares might be sold.
According to reports, the company was looking to raise $8 billion to $10 billion through a listing this year on New York’s technology-heavy Nasdaq platform.
When a firm is listed on a stock exchange, it becomes a public company, and this means that investors can buy and sell shares of the company’s stock on the sale.
Arm, which was established in 1990 in Cambridge, England, is widely regarded as the most valuable asset in the UK’s technology industry.
Arm announced earlier this year that it did not intend to go public on the London Stock Exchange.
Reports in January suggested that UK Prime Minister Rishi Sunak had resumed talks with SoftBank about a possible London listing.
Arm’s decision has raised concerns that the UK market needs to do more to attract stock offerings of technology companies, with US exchanges seen as offering higher profiles and valuations.
The filing shows that SoftBank continues to push ahead with multi-billion dollar sales despite challenging conditions in global financial markets.
The number of stock market listings has decreased significantly since the Russian invasion of Ukraine, and significant technology companies’ shares have also declined due to the pandemic.
SoftBank said the listing was This is dependent on market conditions, other factors, and the SEC’s review process being finished.
It called off SoftBank’s intended $40 billion sale of Arm to technology giant Nvidia last year due to regulatory obstacles in the UK, US, and EU.
Due to the pandemic-induced scarcity of semiconductors, the chipmaking industry is experiencing a decline in demand.
Last week, Intel, a significant chipmaking company in the US, recorded its most considerable quarterly loss ever. In contrast, Samsung, a competing company in South Korea, experienced over a 90% profit decline.
A booming stock market listing of Arm would be welcome news for SoftBank, the owner. Its Vision Funds suffered losses as many of its investments in technology start-ups fell.