Förster Resonance Energy Transfer (FRET) between donor (D) and acceptor (A) molecules is a phenomenon commonly exploited to study or visualize biological interactions at the molecular level. However, commonly used organic D and A molecules often suffer from photobleaching and spectral bleed-through, and their spectral properties hinder quantitative analysis. Lanthanide-doped upconverting nanoparticles (UCNPs) as alternative D species offer significant improvements in terms of photostability, spectral purity and background-free luminescence detection, but they bring new challenges related to multiple donor ions existing in a single large size UCNP and the need for nanoparticle biofunctionalization. Considering the relatively short Förster distance (typically below 5-7 nm), it becomes a non-trivial task to assure sufficiently strong D-A interaction, which translates directly to the sensitivity of such bio-sensors. In this work we propose a solution to these issues, which employs the photon avalanche (PA) phenomenon in lanthanide-doped materials. Using theoretical modelling, we predict that these PA systems would be highly susceptible to the presence of A and that the estimated sensitivity range extends to distances 2 to 4 times longer (i.e. 10-25 nm) than those typically found in conventional FRET systems. This promises high sensitivity, low background and spectral or temporal biosensing, and provides the basis for a radically novel approach to combine luminescence imaging and self-normalized bio-molecular interaction sensing.