Like most 'meanings' it will depend on context.
If you are visiting friends and wander into the kitchen at ten o'clock at night and ask "Is there any book around which I can read?" your hosts will show you the bookcase.
If you are in a bookstore and ask "Is there any book around which I can read?", a salesperson will respond "What sort of book would you like?"
If a question about, say, contemporary trends arises in a course on the History of the English Language and you ask "Is there any book around which I can read?", your professor will respond "Well, you could start with Leech; but drop me an email and I'll send you a bibliography."
Around here means essentially 'readily available'; but what that means will depend on your location and your timeframe.