Cancer spheroids are very effective preclinical models to improve anticancer drug screening. In order to optimize and extend the use of spheroid models, these works were focused on the development of a new storage concept to maintain these models in the longer term using the Triple-Negative Breast Cancer MDA-MB-231 spheroid models. The results highlight that the combination of a temperature of 4 °C and oxygen-free conditions allowed the spheroid characteristics of OptiPASS® serum-free culture medium to preserve the spheroid characteristics during 3-, 5- or 7-day-long storage. Indeed, after storage they were returned to normal culture conditions, with recovered spheroids presenting similar growth rates (recovery = 96.2%), viability (Live/Dead® profiles) and metabolic activities (recovery = 90.4%) compared to nonstored control spheroids. Likewise, both recovered spheroids (after storage) and nonstored controls presented the same response profiles as two conventional drugs, i.e., epirubicin and cisplatin, and two anti-PARP1 targeted drugs—i.e., olaparib and veliparib. This new original storage concept seems to induce a temporary stop in spheroid growth while maintaining their principal characteristics for further use. In this way, this innovative and simple storage concept may instigate future biological sample preservation strategies.