We’re hearing rumors that Google may be shaking things up at the top of its product team for Google+. It’s no secret that the search company has been trying to crack the social puzzle with increasing urgency and desperation.

But now we’ve heard from a single source with direct knowledge of the situation, indicating that the company will hire Dmitry Shapiro as its new head of product for Google+ (or Chief Social Ninja, or whatever they decide to call it).

Shapiro is currently building his own social networking startup Anybeat, previously Altly. Before founding Anybeat, he was the CTO of MySpace Music, which is not exactly a shining example of success in the social networking arena. Previously Shapiro founded and sold two companies in the video and P2P security space to Qlipso and Qwest.

We’ve reached out to Shapiro and to Google for comment. The former was unavailable, while a spokesman for the latter offered the standard, “We don’t comment on personnel issues.”

On that note, Bradley Horowitz has overseen all of Google’s social and communication products since leaving Yahoo in 2008. The Google spokesperson said that this is not a position they’re looking to fill. If anything, this could mean that Shapiro may get a role more siloed within the Google+ product.

This wouldn’t be the first Hail Mary called by Larry Page and crew. In the past, the search giant has acquired Slide (more like acqui-hired Max Levchin and his brainy team), and then shut down the service. Recently they’ve ignored a public outcry over Search Plus Your World, which forced social integration into search. Page even told discontented employees at the time to find somewhere else to work. Most recently, the company threw a life raft to Kevin Rose and his Milk crew, after an underwhelming year operating as a mobile app incubatory.

Google recently has had a habit of skirting the issue of user engagement by only reporting users of “Google Plus-enhanced products”, rather than the social network itself. These figures, which have been reported to be 50 million users per day, actually include anyone logged into a Google account while visiting Google.com, YouTube, or the Android Marketplace. As many observers have pointed out, the only real barometer needed to judge engagement is the answer to the question, “How many people do you know who use Google+?” That answer in most cases has been no one.

According to my source, Shapiro is extremely smart and talented. However, hiring an electrical engineer to lead a social product strikes me as a very Google thing to do. This may just be one man’s opinion, but maybe they could stand to bring someone in with a background in human psychology, communications, or, hell, even sales.

Whoever captains this ship may end up going down with it. But with Google apparently committed to pouring more and more resources into the project, it’s always possible that new blood could turn things around.