Objective: Parkinson’s Disease (PD) is a progressive neurodegenerative disorder, manifesting with subtle early signs, which, often hinder timely and early diagnosis and treatment. The development of accessible, technology-based methods for longitudinal PD symptoms tracking in daily living, offers the potential for transforming disease assessment and accelerating diagnosis. Methods: A privacy-aware method for classifying patients and healthy controls (HC), on the grounds of speech impairment present in PD, is proposed. Voice features from running speech signals were extracted from passively-captured recordings over voice calls. Language-aware training of multiple- and single-instance learning classifiers was employed to fuse and predict on voice features and demographic data from a multilingual cohort of 498 subjects (392/106 self-reported HC/PD patients). Results: By means of leave-one-subject-out cross-validation, the best-performing models yielded 0.69/0.68/0.63/0.83 area under the Receiver Operating Characteristic curve (AUC) for the binary classification of PD patient vs. HC in sub-cohorts of English/Greek/German/Portuguese-speaking subjects, respectively. Out-of sample testing of the best performing models was conducted in an additional dataset, generated by 63 clinically-assessed subjects (24/39 HC/early PD patients). Testing has resulted in 0.84/0.93/0.83 AUC for the English/Greek/German-speaking sub-cohorts, respectively. Conclusions: The proposed approach outperforms other methods proposed for language-aware PD detection considering the ecological validity of the voice data. Significance: This paper introduces for the first time a high-frequency, privacy-aware and unobtrusive PD screening tool based on analysis of voice samples captured during routine phone calls.