Among more than 800 known fast radio bursts (FRBs), only two, namely FRB 20121102A and FRB 20190520B, are confirmed to be associated with persistent radio sources (PRSs). Here, we report evidence of apparent temporal variability in the PRS associated with the bursting FRB 20190520B based on Karl G. Jansky Very Large Array observations taken in 2020 and 2021. Based on the analysis of the epoch-to-epoch variability of the PRS at the L, S, C, and X bands (1–12 GHz), we detected not only overall marginal variability, but also a likely radio flux decrease (σ ∼ 3.2) between the observations taken in 2020 and 2021 at 3 GHz. Assuming no spectral variation in the PRS during these observations, we found evidence for an overall broadband radio flux decrease by about 20% between the 2020 and the 2021 observations, suggesting that the PRS probably evolves on a yearly timescale. If we attribute the marginal variability at 3 GHz as intrinsic or due to scintillation, the size of the potential variable component of the PRS is constrained to be subparsec. On the other hand, the size of the PRS can be also constrained to ≳0.22 pc from the time-averaged radio spectrum and the integrated radio luminosity in the 1–12 GHz band, based on equipartition and self-absorption arguments. We discuss the potential origins of the PRS and suggest that an accreting compact object origin might be able to explain the PRS's temporal and spectral properties. Confirmation of the variability or flux decline of the PRS will be critical for our understanding of the PRS and its relation to the bursting source.