Hydrodesulfurization (HDS) has been commercially employed for the production of ultra-low sulfur fuel oil. However, HDS is unable to remove sterically hindered sulfur-containing compounds such as dibenzothiophene (DBT) and benzothiophene (BT). An alternative way to remove sulfur is via extractive desulfurization system (EDS) using deep eutectic solvents (DES) as sustainable extractant. In this work, liquid polymer DES was synthesized using tetrabutylammonium chloride (TBAC) and poly(ethylene glycol) 400 (PEG) with different molar ratios. Response surface methodology (RSM) was applied to study the effect of independent variables toward extraction efficiency (EE). Three significant operating parameters, temperature (25–70 °C), DES molar ratio (1–3), and DES volume ratio (0.2–2.0), were varied to study the EE of sulfur from model oil. A quadratic model was selected based on the fit summary test, revealing that the extraction efficiency was greatly influenced by the amount of DES used, followed by the extraction temperature and PEG ratio. Although molar ratio of DES was less sensitive towards EDS performance, the EE was much higher at lower PEG ratio. For the realization of an energy-efficient EDS system, optimization of EDS parameters and EE was carried out via a desirability tool. At 25 °C, 1:1 molar ratio of TBAC to PEG, and DES-to-model-oil-volume ratio of 1, removal of DBT reached as high as 79.01%. The present findings could provide valuable insight into the development of practicable EDS technology as a substitute to previous HDS process.