Wine is your best bet. It would be technically possible to make a Linux version of NVDA, but would require rewriting the vast majority of NVDA's code. This is different to say a Word processor where the application is largely self contained and just needs the right hooks into the relavent operating system (How do I call for a save dialog on Linux vs Windows etc). Because NVDA relies on a lot of low-level OS-specific features, it would be a lot of work that we're not planning currently.

There's a well maintained screen reader for Linux graphical environments already. In my opinion, we don't need another. Most of the accessibility issues lie elsewhere (e.g., missing or incorrect accessibility API implementations in system components, UI libraries or applications). I expect that's true of other operating systems too, and there are real limits on what screen reader developers can do to work around those problems - they really need fixing at the source.
I use Linux as a primary operating system every day, so I don't want to give the impression that accessibility is bad there either.