This study investigates the possibility of Atlantic Meridional Overturning Circulation (AMOC) noise-induced tipping solely driven by internal climate variability without applying external forcing that alter the radiative forcing or the North Atlantic freshwater budget. We address this hypothesis with an innovative approach by applying a rare event algorithm to ensemble simulations of present-day climate with an intermediate complexity climate model. The algorithm successfully identifies trajectories leading to abrupt AMOC slowdowns, which are unprecedented in a 2000-year control run. Part of these AMOC weakened states lead to collapsed state without evidence of AMOC recovery on multi-centennial time scales. The temperature and Northern Hemisphere jet stream responses to these internally-induced AMOC slowdowns show strong similarities with those found in externally forced AMOC slowdowns in state-of-the-art climate models. The AMOC slowdown seems to be initially driven by Ekman transport due to westerly wind stress anomalies in the North Atlantic and subsequently amplified by a complete collapse of the oceanic convection in the Labrador Sea. These results demonstrate that transitions to a collapsed AMOC state purely due to internal variability in a model simulation of present-day climate are rare but physically possible. Additionally, these results show that rare event algorithms are a tool of valuable and general interest to study tipping points since they introduce the possibility of collecting a large number of tipping events that cannot be sampled using traditional approaches. This opens the possibility of identifying the mechanisms driving tipping events in complex systems in which little a-priori knowledge is available.