The messaging system, which registers 5 million daily users, would have been Facebook’s most expensive ever acquisition

Snapchat, the fast-growing messaging system, has reportedly rejected a $3bn buyout offer from Facebook.

The Wall Street Journal, citing sources close to the negotiations, said the all-cash offer came as other investors were valuing the loss making two-year-old company at over $4bn. At $3bn Snapchat would be the most expensive acquisition Facebook has ever made.

The company is believed to have over 5 million active daily users and, according to Pew research, has been downloaded by 9% of US mobile users. The service allows people to send messages and photos with an expiration date so that they are deleted from the recipient’s mobile device shortly after they are received. In September Snapchat said it was handling over 350m messages a day.

According to the Journal, Evan Spiegel, Snapchat’s 23-year-old co-founder and chief executive, is waiting until early next year before considering any offers in the hope that Snapchat’s numbers will grow enough to justify an even larger valuation.

The company’s valuation has been growing as fast as its user base. In June Snapchat raised $60m from investors that valued the company at $800m. Facebook reportedly offered $1bn for Snapchat earlier this year. Last month top tech blog All Things D reported that the company was in negotiations with China’s Tencent over an investment that would value the firm at over $3.6bn.

That news followed an announcement last month from Pinterest, the social scrapbooking company, that it had raised $225m in new funds at a price that valued the firm at $3.8bn.

Snapbook’s valuation, and those of its social media peers, will likely have soared after Twitter’s initial public offering this month, which has valued the loss making short message system at over $23bn.

The spectacular growth in the company’s valuation echoes that of Groupon, the online discount company that rejected a $6bn offer from Google before filing for an IPO. In late 2011 when the company started trading it was valued at over $16bn but soon crashed to as low as $3.7bn. It has since recovered and is now worth $6.8bn.