The online social gaming firm Zynga reportedly plans to raise up to $2bn (£1.25bn) with a flotation this week that would value the fledgling internet company at between $15bn and $20bn.

Zynga, the firm behind the hugely popular Facebook games FarmVille and Mafia Wars, will file plans with the US Securities and Exchange Commission as early as Wednesday to become the latest in a gold rush of social media companies to go public, according to CBNC. Zynga initially intends to sell only 10% of its shares in the hope of driving up their valuation, CNBC reported.

The four-year-old gaming firm is expected to become the biggest internet flotation since Google, following sky-high valuations in recent weeks for LinkedIn and the Chinese Facebook', Renren.

Zynga, which announced in May plans to partner with Lady Gaga, says it caters to more than 215 million monthly active gamers selling virtual farm animals for real money.

According to a source reported by the New York Post to have been approached to invest in the San Francisco-based firm in March, Zynga expects to generate $1.8bn in revenue this year – with a profit of $630m. Secondary market estimates put Zynga's 2010 full-year revenues at $850m.

On last year's revenues, a $20bn market cap would value the company at 23 times last year's sales – a higher multiple than the recent big-money technology flotations.

Shares in LinkedIn have soared since it went public last month. The social network for professionals is now valued at $8bn after floating with 2010 revenues of $243m and a profit of $15.4m. Renren has a market cap of $2.98bn after raising $743m with its New York stock exchange debut.

Morgan Stanley is expected to be the lead underwriter on the Zynga IPO, along with Goldman Sachs, Bank of America Merrill Lynch, Barclays and JP Morgan.