A few months ago, Snapchat CEO Evan Spiegel claimed Snapchat had never received a formal acquisition offer from a large company.

That might still be true, but not for lack of interest.

The Wall Street Journal's Evelyn Rusli and Douglas MacMillan say Mark Zuckerberg was willing to pay a lot of money for Spiegel's company — even more than it paid for Instagram. But Spiegel doesn't want to sell his company.

Spiegel and his co-founder, Bobby Murphy, don't need a quick payout. The pair pocketed millions of dollars during previous rounds of financing. So even if Snapchat goes to zero, Spiegel and Murphy will still be millionaires.

"According to people briefed on the matter, Facebook CEO Mark Zuckerberg tried to approach the start-up to discuss an acquisition above $1 billion," Rusli and MacMillan write. "However, Facebook was rebuffed by Spiegel, who was not interested in selling his service to the social network, according to those people." Facebook and Snapchat did not return their requests for comment.

Snapchat is a popular mobile app that lets people take videos or pictures and send them to friends for a short period of time. After a few seconds, the image disappears and can never be viewed again.

If it's a fad, it's a long-lasting one. As of September, Snapchat users were sending 350 million messages per day. That's up from 200 million in June. The company is considering a big new round of financing that could value it between $3 – $4 billion, according to AllThingsD.