Based on investments so far, the California-based firm would be worth between $20bn and $25bn (£16bn-£20n), reports The BBC.
That would make it the largest US flotation since Chinese e-commerce giant Alibaba listed two years ago.
The company began in 2012 as a mobile app that allowed users to send photos that vanish within seconds.
It now has 100 million daily users, which is more than Twitter.
And with 60% of its users aged between 13 and 24, it is seen as an appealing way for advertisers to reach young people.
Snap’s founder, 26-year-old Evan Spiegel, turned down an offer from Facebook founder Mark Zuckerberg to buy Snapchat for $3bn just three years ago.
If it goes ahead, it would be the biggest US technology flotation since Facebook’s $81bn launch in 2012.
According to several reports, Snapchat has filed a confidential application for an initial public offering with the Securities and Exchange Commission.
The US Jumpstart Our Business Startups Act allows companies with less than $1bn in revenue to secretly file.
The idea is that firms can test the appetite among investors, while keeping their finances confidential.
The company has attracted major investors, but with some questioning whether having advertising sales as the only significant form of revenue was sustainable, the firm is branching out.
In September it rebranded itself as Snap, and earlier this month debuted its video-camera sunglasses called Spectacles.
The kit can connect to smartphones and send video and photos to the app.