  Context: Th 28 is a Classical T Tauri star in the Lupus 3 cloud which drives
an extended bipolar jet. Previous studies of the inner jet identified
signatures of rotation around the outflow axis, a key result for theories of
jet launching. Thus this is an important source in which to investigate the
poorly understood jet launching mechanism. We investigate the morphology and
kinematics of the Th 28 micro-jets with the aim of characterizing their
structure and outflow activity, using optical integral-field spectroscopy
observations obtained with VLT/MUSE. We use spectro-imaging and
position-velocity maps to investigate the kinematic and morphological features
of the jet, and obtain a catalogue of emission lines in which the jet is
visible. A Lucy-Richardson deconvolution procedure is used to differentiate the
structure of the inner micro-jet region. Spatial profiles extracted
perpendicular to the jet axis are fitted to investigate the jet width, opening
angle and the evolution of the jet axis. We confirm the previously identified
knot HHW$_{2}$ within the red-shifted jet and identify three additional knots
in each lobe for the first time. We also find [O III]$\lambda$5007 emission
from the blue-shifted micro-jet including the knot closest to the star. Proper
motions for the innermost knots on each side are estimated and we show that new
knots are ejected on an approximate timescale of 10-15 years. The jet axis
centroids show a point-symmetric wiggle within the inner portion of both
micro-jets indicating precession. We use the jet shape to measure a precession
period of 8 years, with a half-opening angle < 0.6$^{\circ}$. This may provide
an alternative explanation for the rotation signatures previously reported. We
find the jet shape to be compatible with precession due to a brown dwarf
companion orbiting at a separation $\leq$ 0.3 au.
