The Google social networking story has moved on with the Wall Street Journal reporting that discussions are being held with games developers to make their games available on the service.

The newspaper names the usual suspects: Zynga, Playfish as well as Playdom, which is being bought by Disney. Only two weeks ago, Google reportedly spent as much as $200m buying a stake in Zynga, which makes Farmville and Café World.

While Google’s social networking site, which is reportedly using the working title of ‘Google Me’,  is widely being reported as a ‘rival’ to Facebook, Eric Schmidt (pictured), the search giant’s chief executive, said this week that “the world doesn’t need a copy” of Facebook.

Although Facebook membership is still growing, longer term users are changing their behaviour on the site.

For what anecdotal evidence is worth, I took my Facebook account down for awhile, but reactivated it because I missed playing Scrabble online (I’ve since been put off Scrabble on Facebook because of the awful new ad overlay, but that’s a whole other blog post – and possibly a couple of apologies to opponents).

If my experience in any way reflects that of other users, it makes sense for Google to put games in a more central role in any new social network. That, and the fact that they tend to be winners when it comes to getting ad revenues.

On the other hand, Google’s previous forays into social networking – Orkut, Google Buzz – have not caught on in the way that googling and Gmail have, so is Google going to get it right this time?