Models with non-gravitational interactions between the dark matter and dark energy components are an alternative to the standard cosmological scenario. These models are characterized by an interaction term, and a frequently used parameterization is $$Q = 3\xi H \rho _{x}$$ Q = 3 ξ H ρ x , where H is the Hubble parameter and $$\rho _{x}$$ ρ x is the dark energy density. Although recent analyses have reported that this particular scenario provides a potential solution to the $$H_{0}$$ H 0 and $$\sigma _{8}$$ σ 8 tensions for negative values of the interaction parameter $$\xi $$ ξ , we show here that such an interval of values of $$\xi $$ ξ leads to a violation of the Weak Energy Condition for the dark matter density, which is accompanied by unphysical instabilities of matter perturbations. Using current observational data we also show that the inclusion of the physical prior $$\xi \ge 0$$ ξ ≥ 0 in the statistical analysis alters the parameter selection for this model and discards it as a solution for the $$H_{0}$$ H 0 -tension problem.