Abstract We report the first Atacama large millimeter/submillimeter array observations of MCG-03-58-007, a local (z = 0.03236 ± 0.00002, this work) AGN ($L_{\mathrm{ AGN}\mathrm{ }}∼ 10^{45}~\rm erg~s^{-1}$), hosting a powerful X-ray ultrafast (v = 0.1c) outflow (UFO). The CO(1-0) line emission is observed across ∼18 kpc scales with a resolution of $∼ 1\, \rm kpc$. About 78 per cent of the CO(1-0) luminosity traces a galaxy-size rotating disc. However, after subtracting the emission due to such rotating disc, we detect with a S/N = 20 a residual emission in the central ∼4 kpc. Such residuals may trace a low velocity (vLOS = 170 km s−1) outflow. We compare the momentum rate ($\dot{P}$) and kinetic power ($\dot{E}$) of such putative molecular outflow with that of the X-ray UFO and find $\dot{P}_{\mathrm{ mol}}/\dot{P}_{\mathrm{ UFO}}∼ 0.4$ and $\dot{E}_{\mathrm{ mol}}/\dot{E}_{\mathrm{ UFO}}∼ 4\times 10^{-3}$. This result is at odds with the energy-conserving scenario suggested by the large momentum boosts measured in some other molecular outflows. An alternative interpretation of the residual CO emission would be a compact rotating structure, distinct from the main disc, which would be a factor of ∼10–100 more extended and massive than typical circumnuclear discs revealed in Seyferts. In conclusion, in both scenarios, our results rule out the hypothesis of a momentum-boosted molecular outflow in this AGN, despite the presence of a powerful X-ray UFO.