Stratified liquid–liquid extraction techniques have piqued attention for separating distinct bio-entities in various bioanalytical systems. This liquid–liquid system uses aqueous polymer or aqueous salt solutions as the background fluid medium. Various external forces can be applied to improve the extraction process. This paper presents an analytical model for a stratified magnetic liquid–liquid microextraction system for Poiseuille flow. In this study, aqueous solutions of polyethylene glycol (PEG) and dextran (DEX) are used to investigate the microextraction system. In the current investigation, a line dipole is precisely positioned outside the microchannel to generate the requisite magnetic field within the microchannel. Magnetic and viscous forces interact to impact the movement of the magnetic microsphere. In this form of liquid–liquid microfluidic system, the Reynolds number (Re) of the carrier and non-carrier phases plays a crucial role in the movement of the microspheres. Two group variables ω and ε are intuitively assumed in order to see the influence of two group variables on the microsphere during their capture and also on interphase height (h). The performance of the device is characterized by capture efficiency (CE). These group variables are found to be exclusive functions of the microsphere capture efficiency (CE). The current work might be very beneficial in simulating a real liquid–liquid microfluidic extraction device.