Alzheimer's disease (AD) is a neurodegenerative condition characterized by a gradual decline in cognitive functions. Currently, there are no effective treatments for AD, underscoring the importance of identifying individuals in the preclinical stages of mild cognitive impairment (MCI) to enable early interventions. Among the neuropathological events associated with the onset of the disease is the accumulation of amyloid protein in the brain, which correlates with decreased levels of Aβ42 peptide in the cerebrospinal fluid (CSF). Consequently, the development of non-invasive, low-cost, and easy-to-administer proxies for detecting Aβ42 positivity in CSF becomes particularly valuable. A promising approach to achieve this is spontaneous speech analysis, which combined with machine learning (ML) techniques, has proven highly useful in AD. In this study, we examined the relationship between amyloid status in CSF and acoustic features derived from the description of the Cookie Theft picture in MCI patients from a memory clinic. The cohort consisted of fifty-two patients with MCI (mean age 73 years, 65% female, and 57% positive amyloid status). Eighty-eight acoustic parameters were extracted from voice recordings using the extended Geneva Minimalistic Acoustic Parameter Set (eGeMAPS), and several ML models were used to classify the amyloid status. Furthermore, interpretability techniques were employed to examine the influence of input variables on the determination of amyloid-positive status. The best model, based on acoustic variables, achieved an accuracy of 75% with an area under the curve (AUC) of 0.79 in the prediction of amyloid status evaluated by bootstrapping and Leave-One-Out Cross Validation (LOOCV), outperforming conventional neuropsychological tests (AUC = 0.66). Our results showed that the automated analysis of voice recordings derived from spontaneous speech tests offers valuable insights into AD biomarkers during the preclinical stages. These findings introduce novel possibilities for the use of digital biomarkers to identify subjects at high risk of developing AD.