Aging results in a progressive decline in skeletal muscle mass, strength and function, a condition known as sarcopenia. This pathological condition is due to multifactorial processes including physical inactivity, inflammation, oxidative stress, hormonal changes, and nutritional intake. Physical therapy remains the standard approach to treat sarcopenia, although some interventions based on dietary supplementation are in clinical development. In this context, thanks to its known anti-inflammatory and antioxidative properties, there is great interest in using extra virgin olive oil (EVOO) supplementation to promote muscle mass and health in sarcopenic patients. To date, the molecular mechanisms responsible for the pathological changes associated with sarcopenia remain undefined; however, a complete understanding of the signaling pathways that regulate skeletal muscle protein synthesis and their behavior during sarcopenia appears vital for defining how EVOO might attenuate muscle wasting during aging. This review highlights the main molecular players that control skeletal muscle mass, with particular regard to sarcopenia, and discusses, based on the more recent findings, the potential of EVOO in delaying/preventing loss of muscle mass and function, with the aim of stimulating further research to assess dietary supplementation with EVOO as an approach to prevent or delay sarcopenia in aging individuals.