selective photodiode transimpedance amplifier
try to optically filter as much unwanted light as possible (e.g. if your LED emits IR use a filter that filters out non-IR light; if your LED emits blue light use a filter that filters out other colors especially IR)
use an amplifier that amplifies only signal changes (AC coupling)
if that is not enough use amplification and band pass filtering (requires knowledge of signal frequency)
if that is not enough use a lock-in amplifier (requires knowledge not only of signal frequency but also of phase)