To investigate the asymptotic giant branch (AGB) population in the Galactic halo, we search for pulsating AGB stars at a heliocentric distance over 50kpc. Our research is based on the Catalina Southern Survey (CSS) catalogue of variables, comprising 1286 long-period variables (LPVs) with declination less than -20{deg}. We first focus on the 77 stars in the cap abs(b)>30deg for which spectral M-type or C-type classification can be derived from Hamburg-ESO objective prism spectra. Most of these are oxygen-rich (M-type) and very few are carbon rich. The periods are in the range 100-500 days, and CSS amplitudes are up to 3mag. In this small sample, no halo AGB star is fainter than Ks0=12.5. This may be due to the scarcity of AGBs in the outer halo, or insufficient instrumental depth. Leaving aside spectral information, we then searched for even fainter pulsators (Ks>12.5) in the entire CSS catalogue. Gaia astrometry makes it possible to identify some contaminants. Our final result is the identification of ten candidate distant LPVs. If these ten stars obey the fundamental mode K-band period luminosity relation used for Miras and small-amplitude Miras, their distances are between 50 and 120kpc from the Sun. In a diagram showing distance versus Gaia tangential velocity, these ten stars have positions similar to those of other objects in the halo, such as globular clusters and dwarf galaxies. We also detect some underluminous AGBs that deserve further study. A detailed catalogue of the 77 high-latitude M or C stars will be made available at the CDS.