Background: Ischemic stroke (IS) often leads to cognitive and motor impairments. This study aimed to investigate whether Memory-Guided Saccade Tasks (MGSTs) could be used to assess cognitive function in stroke patients. Methods: A secondary data analysis was conducted on 62 individuals with supratentorial IS. Eye-tracking metrics from MGST were correlated with established neuropsychological assessments, including the Montreal Cognitive Assessment (MoCA) and Hospital Anxiety and Depression Scale (HADS). Results: Age correlated negatively with memory-guided saccade (MGS) accuracy (ρ = −0.274) and positively with late errors (ρ = 0.327). Higher Montreal Cognitive Assessment (MoCA) scores were associated with faster corrective saccades (ρ = 0.259). Increased anxiety (HADS-A) and depression (HADS-D) levels correlated with higher early error rates (ρ = 0.325 and ρ = 0.311, respectively). The Color Trails Test and Digit Span test performance also correlated with various MGS parameters. Conclusions: While some correlations were found between cognitive measures and eye-tracking metrics, further research is needed to validate MGST as a tool for cognitive assessment in a more homogenous stroke population.