The moon of a transiting exoplanet could be detected directly from the transit it produces itself, or indirectly via the transit timing variations it produces in its parent planet. There is a range of parameter space where the Kepler Space Telescope is sensitive to the TTVs exomoons might produce, though the moons themselves would be too small to detect photometrically via their own transits. The Earth’s Moon, for example, produces TTVs of 2.6 minutes amplitude by causing our planet to move around their mutual center of mass. This is more than Kepler’s short-cadence interval of 1 minute and so nominally detectable (assuming comparable timing accuracy), even though the Moon’s transit signature is only 7% that of Earth’s, well below Kepler’s nominal threshold. Here we explore eight systems from the Kepler data set to examine the exomoon hypothesis as an explanation for their transit timing variations, which we compare with the alternate hypothesis that the TTVs are caused by an non-transiting planet in the system. We find that the TTVs of six of these systems could be plausibly explained by an exomoon that would not be nominally detectable by Kepler. Though we also find that the TTVs could be equally well reproduced by the presence of a non-transiting planet in the system, theobservations are nevertheless completely consistent with a existence of a dynamically stable moon small enough to fall below Kepler’s photometric threshold for transit detection, and these systems warrant further observation and analysis.