Swift is destined to replace Objective-C while still being able to interface with Objective-C/Objective-C++ code-bases. Swift was designed around the LLVM compiler stack while is now available to Apple developers with the Xcode 6 beta. While LLVM is open-source and cross-platform, there's no clear communication that Apple will support such with its new programming language.
Chris Lattner, the founder of LLVM and the one that began developing the Swift programming language in 2010, responded on the Clang mailing list last week, "We don't have anything to say about that at this point [whether Swift will work on non-Mac computers], but you can read all about swift, for free, with the new Swift iBook."
Apple posted this week about job openings on the Swift compiler team. The Apple employee posting the job notice, Ted Kremenek, was asked whether Swift would be open-source. Kremenek responded, "At this time, we honestly don't know the answer yet to that question."