According to Facebook beat writer Josh Constine (along with Drew Olanoff) at TechCrunch, Facebook CEO Mark Zuckerberg said today at the company’s press event that he would “love to work with Google”.

Bing, a longtime partner of Facebook’s is a partner on Graph Search. These are probably not words the search engine (Google’s closest search competitor) really want to hear.

That’s not to say that Facebook and Google will be holding hands anytime soon, but it’s still interesting to see Zuckerberg express this kind of attitude about it. It’s kind of like when Eric Schmidt made similar comments about Yahoo a while back (another partnership that would screw over Bing).

Constine shares a “paraphrased transcription” of what Zuckerberg allegedly said:

I think that the main thing is that when people share something on Facebook we want to give them the ability to broadcast something out and then take it down or set privacy settings. That requires quick updating, removing photos. We also need that content to be gone if something changes their privacy settings.

You need infracture that can support that. Microsoft was more willing to do things that fit with Facebook. People want flexibility, and that was the stumbling block with Google in our last round of talks. I’m not sure if that was detail in the negotiation or rift between Facebook’s and Google’s strategies.

Zuckerberg said in a Q&A (as quoted by The Verge), “We want to work with any company as long as they’ll honor the privacy of the folks on Facebook.”

As long as Facebook and Google aren’t sharing data, Facebook clearly has the upper hand in social. As impressively as Google+ has grown since its launch, it just doesn’t have the connections that Facebook does, and as a result, it just doesn’t have the social data. On the flipside, when it comes to web search, Bing is an adequate alternative to Google in terms of providing web search results to Facebook users. Google may dominate the web search market, but Facebook users who happen to venture to web search results from within the social network probably aren’t that worried about the Google vs. Bing comparison.

Read about Facebook’s new Graph Search here.