When comets and asteroids pass close to the Sun, they release material that can interact with the more homogeneous portion of the interplanetary dust cloud. These interactions may accelerate collisional erosion of the dust cloud. Quantifying the importance of such interactions requires identifying meteoroid streams associated with comets and asteroids in near Sun space, and determining how they interact with the background interplanetary dust cloud. This study uses data recorded by the Parker Solar Probe spacecraft to search for signatures of meteoroid streams in near-Sun space. These data are compared against a model for interplanetary dust, and a localized strong disagreement between the data and model is identified as possibly caused by a meteoroid stream. A handful of asteroids that pass close to the Sun are found to have orbits that could have produced the model-data disagreement. If these asteroids are the source of the observed meteoroid stream, small dry objects like asteroids may shed more material during near-Sun passes than previously understood. Results from this study indicate that asteroid-related meteoroid streams may be common in the near-Sun interplanetary dust cloud, accelerating its evolution by collisions.