Convergence of biodegradability and functionality is a major direction of new generation bio‐based materials. Functionalized aliphatic polyesters based on glycerol are synthesized by solvent‐free polycondensation directly. The aim is to prepare linear polyesters with pendant hydroxyl groups along the polymer backbone. The performance of the sustainable biocatalyst Novozyme‐435 (an immobilized form of Candida antarctica lipase B) and the metal‐based catalyst scandium trifluoromethanesulfonate (also known as scandium triflate) were compared with three organobase catalysts: 1,5,7‐triazabicyclo[4,4,0]dec‐5‐ene, diphenyl hydrogen phosphate, and bis(1,1,2,2,3,3,4,4,4‐nonafluoro‐1‐butanesulfonyl)imide. For the five catalytic systems, the efficiency and selectivity for the incorporation of glycerol were studied, mainly using 1H NMR spectroscopies, whereas side reactions, such as different macromolecular architecture of different glyceride groups in polymers, were evaluated using 13C NMR. Especially, the biocatalyst Novozyme‐435 succeeded in incorporating glycerol in a selective way with a low reaction temperature, leading to close‐to‐linear polyesters. By using a renewable hydroxyl‐reactive based on polyesters derived from glycerol, it provides a theoretical reference for the synthesis of functional bio‐based materials. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48574.