The IPO could take place as early as June. The company wants to raise $75 billion through the Nasdaq listing, sources with knowledge told Bloomberg.
SpaceX is valued at more than $2 trillion - making it the largest IPO to date worldwide.
Founded in 2002 and led by the world's richest man, Elon Musk, the company is a leader in building rockets for space travel and currently supplies both the U.S. space agency NASA and the Pentagon. The company's portfolio also includes satellite systems such as Starlink.
SpaceX's valuation has risen since the company merged with Musk's AI venture XAI in February. XAI, in turn, owns the X platform (formerly Twitter).
Investment banks Goldman Sachs and Morgan Stanley are the lead managers for the IPO, according to Bloomberg. Bank of America, Citigroup and JPMorgan Chase & Co. are also involved.
Terms of the share sale will begin to be disclosed in early June, with pricing on June 11.
At the time of the IPO, SpaceX will be one of the most highly valued companies on the U.S. stock market, larger than, for example, Elon Musk's electric car manufacturer Tesla.
Musk's fortune, currently estimated at $680 billion according to Bloomberg, is expected to grow further.
