Ghost imaging enables the imaging of an object using intensity correlations between a single-pixel detector placed behind the object and a camera that records light that did not interact with the object. The object and the camera are often placed at conjugate planes to ensure correlated illumination patterns. Here, we show how the combined effect of optical reciprocity and the memory effect in a random medium gives rise to correlations between two beams that traverse the random medium in opposite directions. Using these correlations, we demonstrate a ghost imaging scheme in which the object and camera are placed at opposite ends of the random medium and illuminated by counter-propagating beams that can potentially be emitted by two different sources.