Up-to-date cosmological data analyses have shown that textit{(a)} a closed universe is preferred by the Planck data at more than $99%$ CL, and textit{(b)} interacting scenarios offer a very compelling solution to the Hubble constant tension. In light of these two recent appealing scenarios, we consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of state in both the quintessential and phantom regimes. When considering Cosmic Microwave Background data only, a phantom and closed universe can perfectly alleviate the Hubble tension, without the necessity of a coupling among the dark sectors. Accounting for other possible cosmological observations compromises the viability of this very attractive scenario as a global solution to current cosmological tensions, either by spoiling its effectiveness concerning the $H_0$ problem, as in the case of Supernovae Ia data, or by introducing a strong disagreement in the preferred value of the spatial curvature, as in the case of Baryon Acoustic Oscillations.
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