We present a theoretical framework for capturing the coalescence of a pendant drop with a sessile drop in polymeric fluids. The framework is based on the unification of various constitutive laws under a high Weissenberg creeping flow limit. Our results suggest that the phenomenon comes under a new regime, namely, the sub-Newtonian regime followed by the limiting case of arrested coalescence with the arrest angle θarrest ∝ Ec-1/2-1, where Ec-1 is the inverse of Elasto-capillary number. Furthermore, we propose a new time scale T* integrating the continuum variable Ec-1 and the macromolecular parameter Ne, the entanglement density to describe the liquid neck evolution. Finally, we validate the framework with high-speed imaging experiments performed across different molecular weights of poly(ethylene oxide) (PEO).