The messaging app, which allows users to send messages that erase after six seconds, has been valued at $4 billion and the company plans to hold out for an acquisition until at least next year, when it might have an even bigger valuation, said Evan Spiegel, the company's 23-year-old co-founder and CEO.
Facebook, which has built similar products to Snapchat for its platform, previously offered the start-up $1 billion, but then increased its offer and offered all cash, according to the report.
Facebook declined to comment on the matter.
Facebook is no stranger to large acquisitions. The social media giant purchased Instagram for $1 billion last year.
—By CNBC's Cadie Thompson. Follow her on Twitter @CadieThompson.