Cognitive impairments related to changes in the deep gray matter (DGM) and other brain regions occur in up to 70% of patients with multiple sclerosis. Are such brain changes preceded by cognitive decline in patients without clinically evident cognitive impairment? Eighteen participants with relapsing remitting multiple sclerosis (RRMS) and 15 healthy controls took part in this study. Cognitive deficits, depression and fatigue were assessed using the MUSIC test, BDI-II and FSS. FMRI was performed while the participant performed the modified attention network test (ANT). The main analysis concerned the effects of ANT task complexity on the hemodynamic activation of DGMs, including the hippocampus, anterior cingulate cortex (ACC), thalamus, caudate nucleus, pallidum, and putamen. The individual lesion burden was estimated. The group with RRMS showed decreased activation with increasing task complexity in hippocampus, pallidum, and ACC compared to the control group. The thalamus was involved in both group activations but did not differ between groups. Functional changes in the DGM can be detected in RRMS patients before cognitive deficits appear. The affected DGM regions can best be assigned to the Attention Network for Executive Control. This association could serve as a biological indicator of cognitive impairment in MS.