The value of SpaceX once it goes public is expected to surpass $1tn (£751bn). That would make its eventual stock market debut one of the most financially significant in history.
Musk's own holding in SpaceX would put the billionaire on track to become the world's first trillionaire.
The BBC has contacted SpaceX for comment.
The company is aiming to officially go public sometime in June, according to reports in Bloomberg, Reuters and the New York Times.
A confidential IPO filing with the SEC allows a company to avoid immediately revealing information to the public while it requests feedback from the regulator. The next step will be for company executives to hold "roadshows" - meetings with big investors to convince them to buy shares.
