Jung would deduce there cannot be such, and a long history of philology tends to agree with him. Writing is a psychological process, and psychology is anchored in the collective unconscious.
So we are shaped by our culture's shared fund of stories to the degree that we cannot help but be influenced by some 'archetypical' material that would touch upon our mythological roots.
That does not mean the influence is chosen, or that it is even strong. You cannot escape archetypes, but there is all kinds of other material. From a point of view like Jung's (or Lacan's) the very vocabulary is built on exemplars of archetypes, which are older than rational analysis, and therefore mythological. We certainly learn our own language in a matrix of mythologies built on layers of other mythologies. (In Westerns, there is a set of tropes imbued with a mythology of rugged individualism, build on a specific mythologizing of US history and 'American-ness' built on the notion of Christendom, built upon religious positions chosen by Roman Catholics against Orthodox positions chosen to resist Caliphate Islam...) But any story is not just made up of words, or even of basal tropes, or it would completely fail to be art.
In that sense, how does even our non-fiction escape mythological roots?
We derive models in modern sciences by analogy with past models, which ultimately go back to religious impressions. The frequency of particles is the music of the spheres (the songs of angels) and the subtle vibrations of Ayurveda. What is really going on has absolutely nothing to do with vibration, and was originally conceived of as rotation. But we are used to the story, and it has ongoing religious resonance.
We demand a creation myth for our universe, even if it involves an imaginary dimension to time, not because physics actually needs one but because religions always gave us one, and we have come to expect them. (In fact, it is not entirely in accord with the predictive nature of the new views of science to retroactively predict what we will never observe, especially if it requires rules significantly different from the ones we do observe)
And our science is an extension of our philosophy.
Questions here still consider Aristotelian and Platonic views favored by the Church and supportive of a religious creation myth. The whole of our philosophy has been drenched in theology so recently that we are still talking about some 'secular' notion of God, framed as the omnipotent creator, but independent of any acknowledged religious orthodoxy. We make it ontology rather than religion by tying it back to the Greeks.