Late last month we brought you news that Facebook was working on its own search engine. The project reportedly has 24 Facebook engineers working on it, and is headed by none other than Lars Rasmussen, a former Google employee.

Now, though, it looks like this isn’t Facebook’s first foray into the world of search. According to The New York Times, Microsoft actually tried to sell its own search engine, Bing, to Facebook early last year. While there were rumors at the time that they might do so, nothing was ever confirmed. Given that Bing has consistently lost money for Microsoft over the years, several Microsoft execs made overtures to Facebook, with which Microsoft has a remarkably friendly relationship, about taking the search engine off Microsoft’s hands. These overtures, which were not authorized by Microsoft CEO Steve Ballmer, were rebuffed by Facebook CEO Mark Zuckerberg. Zuckerberg declined the offer, saying that Facebook had too much on its plate to worry about such a deal.

Microsoft and Facebook have been growing increasingly cozy with one another over the past few years, likely due to what both companies see as a common enemy: Google. The most recent example of how friendly the two have become is their deal to split the cost of Microsoft’s recent acquisition of AOL’s patents, as well as the patent portfolio itself.

Bing has been a troubled enterprise for Microsoft right from the start. With it, Microsoft aimed to create a serious challenger for Google, and to get itself a piece of the extremely lucrative advertising business that drives Google’s revenues. Unfortunately, Microsoft has consistently lost money on Bing, a fact that apparently doesn’t sit well with some of the company’s higher-ups.

Of course, the possibility of a Facebook search engine adds another interesting wrinkle to the story. Facebook is no doubt taking aim at Google with the project, but by creating its own search engine rather than buying Bing, Facebook could effectively double the amount of competition that Bing faces in the search market. If a Facebook search engine proves popular – and profitable – it could potentially put a strain on Facebook and Microsoft’s cozy friendship.

[H/T: Search Engine Land]