According to Bloomberg, that's exactly what may happen. The social network is in talks with both Cupertino and Redmond to add support for its new Home software suite of apps and services. Facebook product exec Adam Mosseri said in an interview that negotiations are under way, but nothing's set in stone at this point.
Since Apple is such a control freak, though, it seems rather unlikely that Home will ever come to the iPhone in its current form. Home hijacks the home screen and lock screen, as well as numerous key services, and Apple already integrates Facebook directly into iOS, so it may not have much incentive to give up even more control to the social networking giant.
Mosseri entertained the idea of Facebook just building the lock screen, or possibly just modeling the current iOS app to resemble Home. Apple doesn't really have a reason to cede its prime real estate to Facebook, even at a price. Some level of deeper integration could be in the cards, but any offering on par with Home's presence would be too much for the iPhone maker to swallow.
Microsoft has also been rather picky with its Windows Phone platform. The company only taps three different OEMs to date, and has specified a very limited number of supported hardware configurations. Windows Phone already also features deep Facebook integration in its People Hub, and Microsoft even mocked Home after it was unveiled.
One consideration is that Microsoft is invested in Facebook and has closer ties to it than Apple, so it may be more willing to play social ball. Still, the software titan is also likely unwilling to hand over such power for free.
Android is built to be open, so Facebook needed nothing from Google to launch Home, although Google was aware of what Facebook was up to. Facebook didn't have to ink any potentially costly deals with Google, which would probably be table stakes for any Home arrangement with Apple or Facebook.
It might not be called Home, but some type of deeper Facebook integration with both iOS and Windows Phone is a distinct possibility.