Facebook representatives reached out to Snapchat in recent weeks to discuss the all-cash deal, which would have been Facebook's largest acquisition ever, the report said, citing anonymous sources.
Facebook declined to comment. Snapchat could not immediately be reached for comment.
Snapchat, which allows consumers to send smartphone photos which automatically disappear after a few seconds, has proven popular among teenage users.
The report of Facebook's interest in Snapchat comes a couple of weeks after Facebook, the world's No. 1 Internet social network, acknowledged that it was seeing a decline in daily use by young teenagers in the U.S., although it said overall use by teenagers was stable.
Shares of Facebook were up 3.1 percent at $48.05 in afternoon trading on Wednesday.