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Satellites of extrasolar planets, or exomoons, are on the frontier of detectability using current technologies and theoretical constraints should be considered in their search. In this Letter, we apply theoretical constraints of orbital stability and tidal migration to the six candidate KOI systems proposed by Fox & Wigert (2020) to identify whether these systems can potentially host exomoons. The host planets orbit close to their respective stars and the orbital stability extent of exomoons is limited to only $\sim$40% of the host planet's Hill radius ($\sim$20 R$_{\rm p}$). Using plausible tidal parameters from the solar system, we find that four out of six systems would either tidally disrupt their exomoons or lose them to outward migration within the system lifetimes. The remaining two systems (KOI 268.01 and KOI 1888.01) could host exomoons that are within 25 R$_{\rm p}$ and less than $\sim$3% of the host planet's mass. However, a recent independent transit timing analysis by Kipping (2020) found that these systems fail rigorous statistical tests to validate them as candidates. Overall, we find the presence of exomoons in these systems that are large enough for TTV signatures to be unlikely given the combined constraints of observational modeling, tidal migration, and orbital stability. Software to reproduce our results is available in the GitHub repository: Multiversario/satcand.