Speakers usually begin to speak while only part of the utterance has been planned. Earlier work has shown that speech planning processes are reflected in speakers’ eye movements as they describe visually presented objects. However, to-be-named objects can be processed to some extent before they have been fixated upon, presumably because attention can be allocated to objects covertly, without moving the eyes. The present study investigated whether EEG could track speakers’ covert attention allocation as they produced short utterances to describe pairs of objects (e.g., “dog and chair”). The processing difficulty of each object was varied by presenting it in upright orientation (easy) or in upside down orientation (difficult). Background squares flickered at different frequencies in order to elicit steady-state visual evoked potentials (SSVEPs). The N2pc component, associated with the focusing of attention on an item, was detectable not only prior to speech onset, but also during speaking. The time course of the N2pc showed that attention shifted to each object in the order of mention prior to speech onset. Furthermore, greater processing difficulty increased the time speakers spent attending to each object. This demonstrates that the N2pc can track covert attention allocation in a naming task. In addition, an effect of processing difficulty at around 200–350 ms after stimulus onset revealed early attention allocation to the second to-be-named object. The flickering backgrounds elicited SSVEPs, but SSVEP amplitude was not influenced by processing difficulty. These results help complete the picture of the coordination of visual information uptake and motor output during speaking.