We demonstrate an effective approach of modifying the long-range spatial correlation for light propagating inside random photonic waveguides by varying the shape of the waveguide. The functional form of spatial correlation is no longer universal in the regime of diffusive transport and becomes shape dependent due to the nonlocal nature of wave propagation. The spatial dependence of the correlation may become asymmetric for light incident from opposite ends of the waveguide. This work opens the door to control nonlocal effects in mesoscopic transport of waves by tailoring the geometry of random systems. .