Snap Inc. is working on an initial public offering that could value the fast-growing virtual-messaging company at $25 billion or more, making it one of the highest-profile share debuts in years and possibly signaling a turnaround in the new-issue market.

The company, formerly known as Snapchat, is preparing the paperwork for an IPO with a view toward selling the shares as early as late March, according to several people familiar with the matter.

There...