  Metallic Ni$_{1-x}$V$_x$ alloys are known to exhibit a ferromagnetic to
paramagnetic disordered quantum phase transition (QPT) at the critical
concentration $x_c \sim$ 0.114 in bulk. Such a QPT is accompanied by a quantum
Griffiths phase (QGP), the physical observables in which follow non-universal
power-law temperature dependences, in a finite temperature range on the
paramagnetic side of the transition. In the present work, we explore the
occurrence of QGP in nanoparticles of this alloy system. Nanoalloys with $x$ in
the neighbourhood of $x_c$ and mean diameter 18-33 nm were prepared by a
chemical reflux method. Following a few microscopic and spectroscopic studies
to determine the sizes, compositions and phases, dc magnetization measurements
were also performed to seek out any signature of QGP in the nanoalloys. A
paramagnetic-like increase of magnetization is observed to emerge below an
$x$-dependent transition temperature $\rm{T_P} (\it{x})$ within the blocked
ferromagnetic state of the nanoparticles, and is corroborated by a peak at
$\rm{T_P} (\it{x})$ in the temperature dependence of resistivity. The magnetic
susceptibility in this emergent phase follows a non-Curie power-law temperature
dependence below 10 K for $0.09 \leq x \leq 0.14$, indicating the presence of a
QGP in the nanoparticles within these temperature and composition ranges.
