Muonic helium is a hydrogenlike atom composed of a helium atom with one of its two electrons replaced by a negative muon. Its ground-state hyperfine structure is a sensitive tool for testing the theory of three-body atomic systems and bound-state quantum electrodynamics and determining fundamental constants of the negative muon magnetic moment and mass. New precise measurements are now in progress at J-PARC Muon Science Facility (MUSE). Zero-field measurements have already been carried out, and the results are more precise than previous measurements 40 years ago. High-field measurements are now in preparation. Furthermore, a new experimental approach to recover the negative muon polarization lost during the muon cascade process in helium is being investigated, which could drastically improve the measurement accuracy. The first laser repolarization experiments have recently been performed. The status of these new muonic helium HFS measurements and the latest results are presented.