In order to find the most efficient natural solvent for the extraction of quercetin, its solubility was tested in the selected deep eutectic solvents (DESs) such as choline chloride:urea (ChCl:U), choline chloride:glycerol (ChCl:G), citric acid:D-glucose (CA:Glc), citric acid:D-fructose (CA:Frc), lecithin:urea (Lec:U) and lecithin:glycerol (Lec:G), as well as in their aqueous solutions, in a temperature range of 6-75 °C. Quercetin was most successfully dissolved in CA:Frc, followed by ChCl:U and ChCl:G, while CA:Glc was the least efficient. The lecithin-based DESs with urea and glycerol did not dissolve quercetin. The most optimal DES (ChCl:U) was employed in the extraction of quercetin from waste onion (Allium cepa L.) tunic and its efficiency was compared with those of methanol and ethanol. The largest amount of quercetin was extracted with ethanol, followed by methanol and ChCl:U, but quercetin extracted with this DES contained the least amount of impurities. Therefore, the ChCl:U DES was highly recommended for the selective extraction of quercetin.