Future neuroprosthetic devices, in particular upper limb, will require decoding and executing not only the user's intended movement type, but also when the user intends to execute the movement. This work investigates the potential use of brain signals recorded non-invasively for detecting the time before a self-paced reaching movement is initiated which could contribute to the design of practical upper limb neuroprosthetics. In particular, we show the detection of self-paced reaching movement intention in single trials using the readiness potential, an electroencephalography (EEG) slow cortical potential (SCP) computed in a narrow frequency range (0.1-1 Hz). Our experiments with 12 human volunteers, two of them stroke subjects, yield high detection rates prior to the movement onset and low detection rates during the non-movement intention period. With the proposed approach, movement intention was detected around 500 ms before actual onset, which clearly matches previous literature on readiness potentials. Interestingly, the result obtained with one of the stroke subjects is coherent with those achieved in healthy subjects, with single-trial performance of up to 92% for the paretic arm. These results suggest that, apart from contributing to our understanding of voluntary motor control for designing more advanced neuroprostheses, our work could also have a direct impact on advancing robot-assisted neurorehabilitation.