  Recently, several experiments on La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) challenged
the Fermi liquid picture for overdoped cuprates, and stimulated intensive
debates [1]. In this work, we study the magnetotransport phenomena in such
systems based on the Fermi liquid assumption. The Hall coefficient $R_H$ and
magnetoresistivity $\rho_{xx}$ are investigated near the van Hove singularity
$x_{\tiny\text{VHS}}\approx0.2$ across which the Fermi surface topology changes
from hole- to electron-like. Our main findings are: (1) $R_H$ depends on the
magnetic field $B$ and drops from positive to negative values with increasing
$B$ in the doping regime $x_{\tiny\text{VHS}}<x\lesssim0.3$; (2) $\rho_{xx}$
grows up as $B^2$ at small $B$ and saturates at large $B$, while in the
transition regime a "nearly linear" behavior shows up. Our results can be
further tested by future magnetotransport experiments in the overdoped LSCO.
