  The Gelfand-Kirillov dimension measures the asymptotic growth rate of
algebras. For every associative dialgebra $\mathcal{D}$, the quotient
$\mathcal{A}_\mathcal{D}:=\mathcal{D}/\mathsf{Id}(S)$, where $\mathsf{Id}(S)$
is the ideal of $\mathcal{D}$ generated by the set $S:=\{x \vdash y-x\dashv y
\mid x,y\in \mathcal{D}\}$, is called the associative algebra associated to
$\mathcal{D}$. Here we show that the Gelfand--Kirillov dimension of
$\mathcal{D}$ is bounded above by twice the Gelfand--Kirillov dimension of
$\mathcal{A}_\mathcal{D}$. Moreover, we prove that no associative dialgebra has
Gelfand-Kirillov dimension strictly between 1 and 2.
