  Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established
by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a
Mabuchi soliton provided it admits an extremal K\"ahler metric whose scalar
curvature is strictly less than $2(n+1)$. Combined with previous observations
by Mabuchi and Nakamura in the other direction, this gives a characterization
of the existence of Mabuchi solitons in terms of the existence of extremal
K\"ahler metrics on Fano manifolds. An extension of this correspondence to
$v$-solitons is also obtained.
