  We present a pair distribution function (PDF) analysis from neutron
diffraction data of the Ni$_{1-x}$V$_x$ alloy in the Ni-rich regime. Such
structural study aims to clarify the origin of the magnetic inhomogeneities
associated with the quantum Griffiths phase close to the
ferromagnetic-paramagnetic quantum phase transition. The PDF analysis
successfully reveals the details of the structure and chemical distribution of
our Ni$_{1-x}$V$_x$ polycrystalline samples prepared with high-temperature
annealing and rapid cooling protocol. This study confirms the expectations that
all Ni$_{1-x}$V$_x$ samples with 0$ \leq x \leq $0.15 crystallize in a single
phase fcc structure with some residual strain. The increase of the lattice
constant and the atomic displacement parameter with V-concentration $x$ is
consistently explained by a random occupation of V and Ni-atoms on the lattice,
with a radius ratio ($r_{V}/r_{Ni}$) of 1.05. Probing alternate, simple models
of the local PDF, such as V-clusters or ordered structures (Ni$_8$V, Ni$_3$V)
give inferior results compared to a random occupation. This investigation
strongly supports that the magnetic clusters in the binary alloy
Ni$_{1-x}$V$_x$ originate from Ni-rich regions created from "random" occupation
rather than from chemical clusters. It reveals that Ni$_{1-x}$V$_x$ is one of
the rare examples of a solid solution in a wide concentration regime (up to
x=0.15) persisting down to low temperatures (T=15 K).
