Copolymers from ethylene oxide (EO) and propylene oxide (PO) functionalized with glycidyl propargyl ether (GPE) are synthesized. The GPE allows further attachment of drugs but its influence on the polymeric micelle formation is unknown. In this work, the influence of the structure of these copolymers on their critical micellar concentration (CMC) in water and in the size and stability of obtained micelles is studied. For this purpose, the presence of GPE, the copolymer type (gradient or block), the EO:PO ratio and the initiator (water or ethanol) are modified. Gradient copolymers can be synthesized in a single step thanks to the different monomers reactivity, simplifying the process and obtaining similar CMC values to the block copolymers. The use of ethanol as initiator decreases the block copolymer CMC and increases the polydispersity. Besides, the presence of the GPE does not impede the micelle formation and has low effect on the copolymer CMCs. Finally, the higher the EO:PO ratio, the higher the CMC and the smaller the size of micelles. Moreover, Z-potential, DLS and HRSEM analyses show that the micelles are stable, spherical, capable to incorporate coumarin (a hydrophobic drug) and with apparent hydrodynamic sizes suitable to be absorbed by target cells.