Remaining useful life (RUL) is the crucial element in predictive maintenance, helping to reduce significant costs in factories and avoiding production downtime. This work contributes to a non-intrusive condition monitoring to estimate the RUL of the most critical component in an electromechanical system, which does not depend on previous historical run-to-failure data. Although most of the approaches characterize the behavior of the mechanical components from a vibration analysis, this work is focused on monitoring the characteristic frequencies from the torque oscillations that are transmitted via the three-phase stator currents. In this way, several features can be extracted by processing the current signals. Modeling the behavior of the features in a healthy stage, a health indicator is proposed that measures how well a new sample fits the healthy model. This indicator is processed to ensure an indicator with a monotonically increasing trend. Therefore, a procedure is proposed to estimate the RUL by calculating multiple exponential regressions at each sampling time, considering only incremental samples. Based on a defined failure threshold and exponential regressions, a time-to-failure (TTF) non-parametric distribution is updated online, as more samples are processed, the most likely TTF is revealed over time and used to estimate RUL along with its confidence bounds. The proposed approach has been validated with three experiments performed on a run-to-failure ball-bearing testbed, lasting 65 h, 30 h and 180 h. As a result, the methodology achieved high accuracy in anticipating bearing failures 50 h, 26 h, and 100 h before failure; with an accuracy of 93.78%, 89.49% and 64.31%, respectively. A comparative assessment with reported approaches was carried out using the PRONOSTIA-FEMTO datasets, demonstrating the suitable performance of the proposed approach to converge faster to the real RUL with high accuracy.