This study examines molecular interactions between two nanodroplets locating on the graphene monolayer and their morphological transition under the electric field parallel to the monolayer surface by using molecular dynamics simulations. The effects of the electric field and the salt concentration on the transmitted interactions, droplet shape and microscopic structure of interfacial water are elucidated in detail. It was found that the electric field can boost the electrostatic interaction between two pure water (PW) droplets, but weaken the short-range LJ interaction. The electric field with low strength mainly causes separation of two droplets rather than changes their shapes. There is a faster response of microscopic structures of water molecules to strong electric field than the morphological change of droplets, leading to a transition of the interaction energy from strong to weak. The salt concentration in the salty water (SW) droplets has negligible effect on the interaction energy in the absence of electric field. At strong electric field, the break-up behaviors of the SW droplets depend on the salt concentration. Simulation results reveal that the transmitted interactions between the PW and SW droplets as well as two SW droplets significantly affect the break-up behaviors and morphological transition of the droplets.