In this work, we consider a system where external requests arrive for status updates of a remote source, which is monitored by an energy harvesting (EH) sensor. The requests are placed in an aggregator that has direct communication with the sensor and is also equipped with storage space to cache a previously generated status update. A probabilistic model is considered to determine whether a new request will be served with a fresh update from the EH sensor or with a cached update from the aggregator. In the first case, the fresh update will replace the cached one in the aggregator. Assuming that the energy arrivals at the sensor can be modeled by a Bernoulli process, we characterize the average Age of Information (AoI) of the source seen at the aggregator as a function of the external request probability, the battery charging probability, and the probability that a fresh update will be generated by the EH sensor. Our numerical results reveal some insights about the role of caching in EH-based status updating systems.