KM3NeT is a multi-site neutrino telescope under construction in the depth of the Mediterranean Sea, consisting of two Cherenkov telescopes, ARCA and ORCA, both of which are currently in data-taking. Among the primary scientific goals of KM3NeT are the observation of cosmic neutrinos and the investigation of their sources. ARCA and ORCA are optimized in complementary energy ranges, allowing for the exploration of neutrino astronomy from MeV to tens of PeV. The combination of an extended field of view and a high duty cycle of Cherenkov-based neutrino detectors is crucial for detecting and informing other telescopes about interesting neutrino candidates in a very short time. As emission from these sources can rapidly fade, the alerts need to be shared with low latency, in order to allow for a prompt follow-up in the multi-messenger and multi-wavelength domains, particularly for the detection of transient and variable sources. In the case of poorly localized triggers, such as gravitational waves, KM3NeT can provide refined pointing directions, representing a further advantage. This contribution reports on the status of the software architecture implemented in KM3NeT for a fast reconstruction and classification of events occurring in the detectors. Additionally, the results of the online processing of KM3NeT data in coincidence with GRB221009A will be presented.