In liquid-phase microextraction (LPME), the sample and the acceptor are separated by a synthetic organic solvent, which is immobilized in a porous polymeric membrane of polypropylene or polyvinylidene fluoride. The organic solvent serves as extraction phase, while the polymeric membrane serves as support membrane. The combination of extraction phase and support membrane is termed supported liquid membrane (SLM). In this paper, we developed for the first time fully green and biodegradable supported SLMs, based on natural deep eutectic solvents as extraction phase and agarose as support membrane. This highly green approach was developed and studied with sulfonamide pharmaceuticals as model analytes, and performance was compared with LPME using conventional SLMs. All experiments were conducted in a microfluidic device. Model analytes were extracted from acidic sample (pH1.0) and into alkaline acceptor (pH12.0). Both sample and acceptor were pumped at 1 μL min⁻¹ into the microfluidic device, and the optimal SLM was based on 3 µL of coumarin and thymol (1:2 molar ratio) as the extraction phase. The proposed green microfluidic device was successfully applied for the determination of sulfonamides in urine samples with spiking recoveries in the range of 77–100%. LPME with deep eutectic solvent immobilized in agarose showed similar performance as with conventional SLMs. Thus, the data presented in this paper demonstrate that highly green microextraction systems may be developed in the future, based on natural solvents and biodegradable materials.