  Context. The inner few au region of planet-forming disks is a complex
environment. High angular resolution observations have a key role in
understanding the disk structure and the dynamical processes at work. Aims. In
this study we aim to characterize the mid-infrared brightness distribution of
the inner disk of the young intermediate-mass star HD 163296, from VLTI/MATISSE
observations. Methods. We use geometric models to fit the data. Our models
include a smoothed ring, a flat disk with inner cavity, and a 2D Gaussian. The
models can account for disk inclination and for azimuthal asymmetries as well.
We also perform numerical hydro-dynamical simulations of the inner edge of the
disk. Results. Our modeling reveals a significant brightness asymmetry in the
L-band disk emission. The brightness maximum of the asymmetry is located at the
NW part of the disk image, nearly at the position angle of the semimajor axis.
The surface brightness ratio in the azimuthal variation is $3.5 \pm 0.2$.
Comparing our result on the location of the asymmetry with other
interferometric measurements, we confirm that the morphology of the $r<0.3$ au
disk region is time-variable. We propose that this asymmetric structure,
located in or near the inner rim of the dusty disk, orbits the star. For the
physical origin of the asymmetry, we tested a hypothesis where a vortex is
created by Rossby wave instability, and we find that a unique large scale
vortex may be compatible with our data. The half-light radius of the L-band
emitting region is $0.33\pm 0.01$ au, the inclination is
${52^\circ}^{+5^\circ}_{-7^\circ}$, and the position angle is $143^\circ \pm
3^\circ$. Our models predict that a non-negligible fraction of the L-band disk
emission originates inside the dust sublimation radius for $\mu$m-sized grains.
Refractory grains or large ($\gtrsim 10\ \mu$m-sized) grains could be the
origin for this emission.
