Background: The assessment of language deficits can be valuable in the early clinical diagnosis of neurodegenerative disorders, including Alzheimer’s disease (AD). Objective: The present study aims to explore whether language markers at the macrostructural level could assist with the placement of an individual across the dementia continuum employing production data from structured narratives. Methods: We administered a Picture Sequence Narrative Discourse Task to 170 speakers of Greek: young healthy controls (yHC), cognitively intact healthy elders (eHC), elder participants with subjective cognitive impairment (SCI), with mild cognitive impairment (MCI), and with AD dementia at the mild/moderate stages. Structural MRIs, medical history, neurological examination, and neuropsychological/cognitive screening determined the status of each speaker to appropriately groupthem. Results: The data analysis revealed that the Macrostructure Index, Irrelevant Info, and Narration Density markers can track cognitive decline and AD (p < 0.001; Macrostructural Index: eHC versus AD Sensitivity 93.8%, Specificity 74.4%, MCI versus AD Sensitivity 93.8%, Specificity 66.7%; Narration Density: eHC versus AD Sensitivity 90.6%, Specificity 71.8%, MCI versus AD Sensitivity 93.8%, Specificity 66.7%). Moreover, Narrative Complexity was significantly affected for subjects with AD, Irrelevant Info increased in the narrations of speakers with MCI and AD, while Narration Length did not appear to indubitably differentiate between the cognitively intact groups and the clinical ones. Conclusions: Narrative Macrostructure Indices provide valuable information on the language profile of speakers with(out) intact cognition revealing subtle early signs of cognitive decline and AD suggesting that the inclusion of language-based assessment tools would facilitate the clinical process.