To expand Zeiss Ikon reply, metal wire data storage devices existed at some point in the late 40's (according to this Ars technica article, you can see them in "The Thing"). One would argue that the first use of these kind of devices (in 1898) was precisely data storage: the first patent covers a telegraph log recorder. Voice dictation would come after the invention of the microphone.
Self-looping data tape devices also existed, such as the ZX Microdrive.
Both devices are known for one thing: unreliability. Thread is very thin and prone to breakage, and looping devices (of any nature) can tangle and break, too.
So combining both is not a very good idea.
So, is possible? yes, and is perfect if your novel is set in the 40's or earlier.
Is practical? not much. There's a good reason we stopped using them. Information density is not good and they are prone to breakages. It may be slightly easier to manufacture, but not much more than tape.
Edit: I would add that one could argue that magnetic platters are the pinnacle of magnetic wire storage: it is, after all, a series of concentric rings of magnetic loop, fused so they can spin faster than any wire would do, but that's outside the scope of the question ;)
Edit2: In general you want as less moving pieces as possible. That's why we moved from tapes to disks and from discs to solid state devices :)