  We study some properties of the $3$-dimensional manifold $\mathbb R^3$ with a
diagonal Riemannian metric as an almost $\eta$-Ricci soliton from the following
points of view: under certain assumptions, we determine the potential vector
field if $\eta$ is given; we get obstructions on the metric when the potential
vector field has a particular expression; we compute the defining functions of
the soliton when both the potential vector field and the $1$-form are
prescribed. Moreover, we find conditions for the manifold to be flat or
Ricci-flat. Based on the theoretical results, we provide examples.
