We present an automated method for finding feasible placements of regions on partially reconfigurable Field-Programmable Gate Arrays (FPGAs). Such reconfigurable regions are placed at design time, and can be allocated to different modules at run time. We consider regions that support relocatable modules. A model is introduced that enables masking out non-matching resources for relocatable modules, with an algorithm to find a suitable region placement for such modules. We also consider communication constraints and fragmentation. In a case study involving software-defined radio, we demonstrate that our algorithm increases the number of relocatable regions that can be placed on a device. The average configuration storage size is reduced by a factor of 5.2 when using the proposed relocation approach, which also leads to improvement in compilation time.