The anionic polymer sodium alginate, a linear copolymer of guluronic and mannuronic acids, is primarily present in brown algae. Copolymers are used in the sodium alginate preparation process to confer on the material strength and flexibility. Micelles and other polymeric nanoparticles are frequently made using the triblock copolymer Pluronic®F-127. The purpose of the present study is to determine the effect of sodium alginate’s viscosity (low and medium) and the presence of Pluronic®F-127 micelles on the swelling behavior of the prepared pure beads and those loaded with Pluronic®F-127 micelles. The Pluronic®F-127 nanomicelles have a size of 120 nm. The swelling studies were carried out at pH = 1.2 (simulated gastric fluid-SGF) for two hours and at pH = 6.8 (simulated intestinal fluid-SIF) for four more hours. The swelling of both low- and medium-viscosity alginate beads was minor at pH = 1.2, irrespective of the use of Pluronic®F-127 nanomicelles. At pH = 6.8, without Pluronic®F-127, the beads showed an enhanced swelling ratio for the first four hours, which was even higher in the medium-viscosity alginate beads. With the addition of Pluronic®F-127, the beads were dissolved in the first and second hour, in the case of the low- and medium-alginate’s viscosity, respectively. In other words, the behavior of the mixed hydrogels was the same during the swelling experiments. Therefore, the presence of Pluronic®F-127 nanomicelles and medium-viscosity sodium alginate leads to a higher swelling ratio. A model drug, acetyl salicylic acid (ASA), was also encapsulated in the mixed beads and ASA’s release studies were performed. In conclusion, the prepared systems, which are well characterized, show potential as delivery platforms for the oral delivery of active pharmaceutical ingredients and biopharmaceuticals.