  Three-dimensional van der Waals ferromagnet Fe$_3$GeTe$_2$ (FGT) is regarded
as a candidate for the magnetic topological nodal line semimetal. We
investigate lateral electron transport between two 3~$\mu$m spaced
superconducting In leads beneath a thick three-dimensional FGT exfoliated
flake. At low 30~mK temperature, we observe Josephson supercurrent that
exhibits unusual critical current $I_c$ suppression by the magnetic field $B$.
The overall $I_c(B)$ pattern is asymmetric in respect to the B sign. We
demonstrate, that the asymmetry is defined by the magnetic field sweep
direction, so the $I_c(B)$ pattern is strictly reversed (as $B$ to $-B$
inversion) for the opposite sweeps. We also observe an interplay between
maximum and minimum in $I_c(B)$ in normal magnetic fields, while there are fast
aperiodic $I_c(B)$ fluctuations for the in-plane ones. These effects can not be
expected for homogeneous superconductor-ferromagnet-superconductor junctions,
while they are known for Josephson spin valves. The mostly possible scenario
for Josephson spin valve realization in FGT is the misalignment of spin
polarizations of the Fermi arc surface states and ferromagnetic FGT bulk, but
we also discuss possible influence of spin-dependent transport between magnetic
domains.
