Mutations in the TP53 gene, a key tumor suppressor involved in DNA repair and cell cycle regulation, are among the most frequent alterations in human cancers. While TP53 mutagenesis can involve biochemical mechanisms such as methylation and oxidative damage, recent theoretical studies have proposed that quantum mechanical properties of DNA, particularly quantum entanglement, may influence mutation susceptibility in general. Whether such quantum effects contribute to mutational patterns in specific genes such as TP53 remains unexplored. In this exploratory study, we applied a coupled quantum harmonic oscillator model to quantify site-specific von Neumann Entropy (VNE), a proxy for quantum entanglement, across the TP53 sequence. Our findings show that known mutation hot spots exhibited significantly elevated VNE compared to non-hot spot regions, suggesting enhanced local quantum coupling may reflect increased structural instability or altered repair dynamics. CpG sites did not exhibit a similar statistically significant elevation in VNE, suggesting that CpG methylation-associated mutability may not be directly linked to the quantum entanglement properties captured by our closed model. These results are a computational demonstration of a potential quantum mechanical contribution to genomic instability in TP53. This indicates further work on expanding the conceptual framework of cancer mutagenesis to include biophysical determinants may be warranted. We note this analysis is limited by the small number of validated hot spots (n=6) and the lack of biological validation, and the findings should be interpreted cautiously pending larger-scale validation. Such validation could include additional genes and biophysical measurements. We urge further interdisciplinary approaches between quantum physics and molecular oncology to explore new ways to understand mutation patterns, improve hot spot prediction, and inform future diagnostic or therapeutic strategies targeting genome stability.