Organic semiconductors are commonly used as charge-extraction layers in metal-halide perovskite solar cells. However, parasitic light absorption in the sun-facing front molecular layer, through which sun light must propagate before reaching the perovskite layer, may lower the power conversion efficiency of such devices. Here, we show that such losses may be eliminated through efficient excitation energy transfer from a photoexcited polymer layer to the underlying perovskite. Experimentally observed energy transfer between a range of different polymer films and a methylammonium lead iodide perovskite layer was used as basis for modelling the efficacy of the mechanism as a function of layer thickness, photoluminescence quantum efficiency and absorption coefficient of the organic polymer film. Our findings reveal that efficient energy transfer can be achieved for thin (≤10 nm) organic charge-extraction layers exhibiting high photoluminescence quantum efficiency. We further explore how the morphology of such thin polymer layers may be affected by interface formation with the perovskite.