The collision of particles sedimenting in a flow field is relevant to many environmental and industrial processes. Applications include the growth of water droplets in warm clouds, dust storms, aggregation of soot particles during industrial emissions, and combustion in engines. More importantly, the lack of physically correct parameterization of collisional growth of cloud drops is a prime source of uncertainty in weather forecasting and climate models. The evolution of the particle size distribution in such systems crucially depends on the collision rate between the particles, where the combined effect of background flow, gravity, and interparticle interactions drive the collision dynamics. A study of this problem might explain the condensation-coalescence bottleneck (or the ‘size gap’ of 15 - 40 μm droplets) in warm rain formation, where neither condensation nor gravitational collision alone is the dominant growth mechanism. The present study focuses on estimating the collision efficiency in a background flow coupled with gravity and modulated by hydrodynamic interactions. The continuum assumption of hydrodynamic interactions fails at close separations, and the near-field non-continuum interactions become the dominant mechanism for collisions in media with long mean-free paths, like air. We calculate the collision efficiency of two inertia-less spheres interacting through non-continuum hydrodynamics and sedimenting in a simple shear flow. We also predict the collision efficiency of hydrodynamically interacting spheres settling rapidly in a homogeneous isotropic turbulent flow.