FIPS 140-2 does not cover the topic of password hashing. Thus, there is no password hashing function which would be "FIPS-approved" in that sense. Using SHA-512 "as is", with or without some salt and regardless of how you inject the said salt in the engine, would not grant you the NIST approval. NIST simply does not approve (or disapprove of) password hashing.
The closest you can get in the NIST world is SP 800-132, that lists approved methods for password-based key derivation, something which is quite close (but not identical) to password hashing. NIST approves PBKDF2, as long as the underlying primitive used in PBKDF2 is itself "approved" (i.e. it is HMAC used with one of the SHA-2 functions).