This study investigated the relationship between lower limb muscle strength and temporal preparation in older adults using an electroencephalogram to assess neural oscillations during cognitive processes. Forty older adults were divided into higher (HSG, 70.40 ± 5.15 years) and lower muscle strength (LSG, 71.43 ± 4.86 years) groups based on quadriceps strength estimated via a manual muscle test. Functional mobility was assessed using the Timed Up and Go (TUG) test, while temporal preparation was evaluated using a choice response time (RT) task with randomly varying foreperiods (FPs) that required lower limb motor responses. The HSG outperformed the LSG on both the TUG test (HSG: 6.07 ± 1.14 vs. LSG: 6.79 ± 0.88, p = 0.031) and the cognitive task (HSG: 462.97 ± 51.06 ms vs. LSG: 525.86 ± 73.69 ms, p = 0.002), despite no clear FP effect in either group. Additionally, the HSG demonstrated a more pronounced modulation of oscillatory beta power during the late phase of longer FP trials (qs < 0.05, FDR corrected), whereas no significant modulation was observed during shorter FP trials. Crucially, mediation analysis indicated that beta power significantly mediated the relationship between lower limb strength and RT in longer FP trials [b = -24.21; 95% CI = (-53.51, -0.24)]. In summary, these findings suggest that lower limb strength may influence the development of temporal preparation during longer preparatory periods by modulating beta power, potentially serving as a compensatory mechanism to mitigate age-related declines in cognitive processing speed and preserve functional mobility.