According to Bloomberg, Facebook is currently in talks with Apple to bring Facebook Home to the iPhone. Mind you, that doesn't mean we should expect Facebook Home to actually come to the iPhone (as that seemingly wouldn't jive with Apple's MO) but it does show Facebook's obvious desire to bring more Facebooking to more phones.
Adam Mosseri, director of product at Facebook, told Bloomberg that Facebook has shown Apple what it has built and is participating in an "ongoing conversation" and an "active dialogue" with Cupertino about Facebook Home. Mosseri warns not to expect the Android version of Facebook Home ported over to iOS though:
"It may or may not be Home. We could also just bring some of the design values to the iOS app. That might be how it ends up. Or we could build just the lock screen. Maybe then it's not called Home, it's called something else."
Facebook has also been talking with Microsoft about Facebook Home which makes it clear that Facebook—for the moment at least—would much rather create Facebook-centric experiences through software on other company's phones instead of making a real Facebook phone. [Bloomberg]