Frontal EEG asymmetry has been investigated as a physiological metric of approach motivation, with higher left frontal activity (LFA) suggested to reflect approach motivation. However, correlations between LFA and traditional metrics of approach motivation (e.g., scores from the behavioral inhibition system/behavioral approach system [BIS/BAS] survey) are inconsistent. It is also not clear how LFA correlates to approach motivation on an observable, behavioral level. Here, we tested correlations between BIS/BAS scores, LFA, and performance in the Effort Expenditure for Rewards Task (EEfRT). In our sample (n = 49), BIS/BAS results did not correlate to LFA values (resting or task states), and were also unrelated to EEfRT performance variables. We found evidence of significant and distinct correlations between LFA and EEfRT performance. Resting-state LFA positively correlated to effort expenditure on lower utility trials, where reward size and/or probability were suboptimal. Task-onset LFA captured in the first 5 min of the task was related to overall behavioral performance in the EEfRT. High task-onset LFA correlated to high trial completion rates, high-effort trial selection percentages, and overall monetary earnings. One interpretation of these initial findings is that resting-state LFA reflects approach tendencies to expend effort, but that this extends to suboptimal situations, whereas task-state LFA better reflects effortful approach toward high-utility goals. Given the relatively small sample size and the risk of Type I/II errors, we present the study as exploratory and the results as preliminary. However, the findings highlight interesting initial links between LFA and EEfRT performance. The need for larger replication studies is discussed.