Approximate entropy (ApEn) is used as a nonlinear measure of heart-rate variability (HRV) in the analysis of ECG time-series recordings. Previous studies have reported that HRV can differentiate between frail and pre-frail people. In this study, EEGs and ECGs were recorded from 38 elderly adults while performing a three-stage cycling routine. Before and after cycling stages, 5-min resting-state EEGs (rs-EEGs) and ECGs were also recorded under the eyes-open condition. Applying the K-mean classifier to pre-exercise rs-ECG ApEn values and body weights revealed nine females with EEG power which was far higher than that of the other subjects in all cycling stages. The breathing of those females was more rapid than that of other subjects and their average heart rate was faster. Those females also presented higher degrees of asymmetry in the alpha and theta bands (stronger power levels in the right frontal electrode), indicating stressful responses during the experiment. It appears that EEG delta activity could be used in conjunction with a very low ECG frequency power as a predictor of bursts in the heart rate to facilitate the monitoring of elderly adults at risk of heart failure. A resting ECG ApEn index in conjunction with the subject’s weight or BMI is recommended for screening high-risk candidates prior to exercise interventions.