Last month, rumors emerged about a potential Google social network – dubbed Google Me. While Google remains mum about whether it is developing a social site, the company seems to be moving forward with its social network game plan – literally. The Wall Street Journal reports that Google execs have been courting top interactive game developers.

The games would be part of Google’s broader social platform, anonymous insiders told the newspaper. Google has reportedly been speaking with Playdom, Electronic Arts and Zynga Game Network. Notably, Zynga is the developer behind FarmVille – a popular Facebook game. Multiple reports indicate Google recently invested in Zynga – perhaps hundreds of millions of dollars, says TechCrunch.

If these reports are true, Google’s social network could be positioning itself as a powerful player in the ever-growing social media channel – the social gaming market is expected to reach $2 billion by 2012, according to reports from ThinkEquity. Importantly, tapping into the rise of the social game industry could help Google Me stand as a viable competitor for social giant Facebook.

Though Google’s move into social gaming may be an effort to capture the interest of users and advertisers who are flocking to Facebook, officials make it clear that Google wants to set itself apart from Facebook. Google CEO Eric Schmidt remains tight-lipped about if and when Google Me will launch, but he responded to the WSJ’s inquiry about how Google’s services will resemble Facebook by saying, “the world doesn’t need a copy of the same thing.”

Nonetheless, Google execs may be concerned over the leverage Facebook has recently had over the search engine. Zuckerberg’s social site garnered more visits than Google for the first time ever in March 2010, reports Hitwise. Facebook has also improved its offerings for marketers on the platform. Plus, the site just launched Facebook Questions – a question-and-answer service that addresses some of the same needs as search engines (though with arguably lesser degrees of credibility).

For now, the company need not fret – the latest web property rankings from comScore show that Google sites took the lead in June 2010, with more than 178 million unique visitors. Meanwhile ranked fourth with around 140 million visitors.