I don't know of anything currently available (and wouldn't have cause to find out, since I like my Linux desktop
).
But
calibre is currently undergoing a massive rewrite around the Content Server, for the calibre v3 milestone, and as part of that rewrite it is expected that you will be able to read/write to the library from the browser.
You'd still have to run calibre on a dedicated server. Also, it is not ready yet (at all).
But in an upcoming calibre v3 you might have your solution.