Interactions between a droplet and an immiscible liquid surrounding it profoundly influence its dynamics and shape deformation. These characteristics are essential in droplet manipulation utilized in a wide range of industrial applications. To comprehend the effect of various forces synergistically impact the droplet manipulation phenomenon, a two-phase flow of a single droplet within a microchannel as a case study is considered in the present investigation. To do so, herein, The Physics-Informed Neural Network (PINN), as an innovative method for solving complicated multiphysics problems described based on coupled partial differential equations (PDEs), is employed. The PDE system for two-phase flow consists of the continuity equation, the Navier-Stokes equations, and the Volume of Fluid (VOF) model equation. The continuity and Navier-Stokes equations govern the flow of main and droplet fluids through the microchannel, whereas the VOF model is utilized to describe the interactions between the droplet and the main flow, as well as track the interface. The fully connected neural network is trained using the Adam optimization algorithm. The results are validated with Computational Fluid Dynamics (CFD) methods. This work provides a novel framework, offering promising implications for applications where accurate interface tracking is critical for effective droplet manipulation, and it also provides valuable insight into the use of PINNs for two-phase flow simulations.