It has been shown by \textit{Scherrer and Putter et.al} that, when dynamics

of dark energy is driven by a homogeneous $k-$essence scalar field $\phi$, with

a Lagrangian of the form $L = V_0F(X)$ with a constant potential $V_0$ and $X =

\frac{1}{2}\nabla^\mu\phi \nabla_\mu\phi = \frac{1}{2}\dot{\phi}^2$, one

obtains a scaling relation $X(dF/dX)^2 = Ca^{-6}$ , where $C$ is a constant and

$a$ is the FRW scale factor of the universe. The separate energy conservation

in the dark energy sector and the constancy of $k-$essence potential are

instrumental in obtaining such a scaling. In this paper, we have shown that

even when considering time-dependent interactions between dark energy and dark

matter, the constancy of $k-$essence potential may lead to a modified form of

scaling. We have obtained such a scaling relation for a particular class of

parametrisation of the source term occurring in the continuity equation of dark

energy and dark matter in the interacting scenario. We used inputs from the JLA

analysis of luminosity distance and redshift data from Supernova Ia

observations, to obtain the modified form of the scaling.