The interest on wearable textiles to monitor vital signs is growing in the research field and clinical scenario related to the increasing demands of long-term monitoring. Despite several smart textile-based solutions have been proposed for assessing the respiratory status, only a limited number of devices allow the respiratory monitoring in a harsh environment or in different positions of the human body. In this paper, we investigated the performances of a smart textile for respiratory rate monitoring characterized by 12 fiber optic sensors (i.e., fiber Bragg grating) placed on specific landmarks for compartmental analysis of the chest wall movements during quiet breathing. We focused on the analysis of the influence of sensor position on both peak-to-peak amplitude of sensors output and accuracy of respiratory rate measurements. This analysis was performed on two participants, who wore the textile in two positions (i.e., standing and supine). Bland-Altman analysis on respiratory rate showed promising results (better than 0.3 breaths per minute). Referring to the peak-to-peak output amplitude, the abdomen compartment showed the highest excursions in both the enrolled participants and positions. Our findings open up new approaches to design and develop smart textile for respiratory rate monitoring.