To achieve a seamless human-robot collaboration, it is crucial that robots express their intentions without perturbating or interrupting the task that a human partner is performing at that moment. Although it has not received much attention so far, this issue is important when robots assist humans in physical and manipulation tasks. The main question addressed here is whether there is a more appropriate time to inform a human partner that a robot is requesting to pass them an object. This question is posed in a reference scenario where human individuals are involved in a continuous pick-and-place task that cannot be interrupted. Our findings showed that providing a cue at the beginning of a reach-to-grasp movement could severely interfere with the ongoing human action, increasing the number of errors made by humans, slowing down and degrading the smoothness of their arm movement, and deflecting their gaze. These disruptive interferences strongly decreased, until they disappeared, when the robot provided the cue to the human partners shortly after the participants picked up an object, identifying this as the best signaling timing. The results of this work showed how the signaling timing may have a decisive influence on the performances of the human-robot teamwork and contribute to understanding the mechanisms underpinning the phenomenon of cognitive-motor interference in humans.