The KM3NeT Collaboration is constructing two large neutrino detectors in the Mediterranean Sea: ARCA, located near Sicily and aiming at neutrino astronomy, and ORCA located near Toulon and designed for the study of intrinsic neutrino properties (neutrino oscillations, mass ordering, etc.). The two detectors together will have hundreds of Detection Units (DUs) with Digital Optical Modules (DOMs) kept vertically by buoyancy forming a large 3D optical array for detecting the Cherenkov light produced after the neutrino interactions. To properly reconstruct the direction of the incoming neutrino, the position of the DOMs, which are not static due to the sea currents, must be monitored. For this purpose, the detector is equipped with an Acoustic Positioning System, which is composed of fixed acoustic emitters on the sea bottom, a hydrophone in each DU base, and a piezoceramic sensor in each DOM, as acoustic receivers. This network of acoustic sensors can be used not only for positioning, but also for acoustic monitoring studies such as bioacoustics, ship noise monitoring, environmental noise control, and acoustic neutrinos detection. This work explores the possibility of creating a trigger for saving the data for ultra-high-energy neutrino candidates detected acoustically by the hydrophones. The acoustic signal caused by the neutrino interaction in a fluid is a short-time duration Bipolar Pulse (BP) extremely directive and with a Fourier transform extending over a wide range of frequencies. A study of signal detection, out of the background, has been done by simulating BP produced by the interaction of a 10$^{20}$ eV neutrino at 1 km from the detector at zero-degree incidence added to the experimental real acoustic data. Finally, a trigger proposal has been developed in order to record candidates of BPs and it has been tested. The number of candidates per second, precision, and recall have been monitored according to the cuts applied and parameters calculated by the algorithm