  A probability distribution $\mu$ on $\mathbb{R}^d$ is quasi-infinitely
divisible if its characteristic function has the representation $\widehat{\mu}
= \widehat{\mu_1}/\widehat{\mu_2}$ with infinitely divisible distributions
$\mu_1$ and $\mu_2$. In \cite[Thm. 4.1]{lindner2018} it was shown that the
class of quasi-infinitely divisible distributions on $\mathbb{R}$ is dense in
the class of distributions on $\mathbb{R}$ with respect to weak convergence. In
this paper, we show that the class of quasi-infinitely divisible distributions
on $\mathbb{R}^d$ is not dense in the class of distributions on $\mathbb{R}^d$
with respect to weak convergence if $d \geq 2$.
