Interactions between Atlantic and Pacific Oceans can affect tropical Pacific variability and its global impacts at both interannual and decadal timescales. Thus, a deepened understanding of the coupled Atlantic-Pacific interactions is needed. While possible dynamical mechanisms by which the Atlantic can influence the Pacific have been identified, the effectiveness of those mechanisms is difficult to establish using climate model simulations where Atlantic sea surface temperatures (SSTs) are prescribed and Pacific feedbacks cannot be realistically included. As an alternative approach, here we use a Linear Inverse Model (LIM) trained on observations and capable of correctly reproducing the observed statistics, to assess the relative role of the Atlantic-to-Pacific and Pacific-to-Atlantic influences on tropical Pacific variability. Our results indicate that Atlantic internal variability can enhance interannual SST anomalies in the eastern equatorial Pacific, and decadal SST anomalies in the central equatorial Pacific, while Pacific influences on the Atlantic significantly damp tropical Pacific decadal variability. This methodological framework could also be used to assess climate model fidelity in representing tropical basin interactions, helping to reconcile existing differences among models’ results.