Interlocutors often use the semantics of comprehended speech to inform the semantics of planned speech. Do representations of the comprehension and planning stimuli interact? In this EEG study, we used rapid invisible frequency tagging (RIFT) to better understand the attentional distribution to representations of comprehension and speech planning stimuli, and how they interact in the neural signal. To do this, we leveraged the picture-word interference (PWI) paradigm with delayed naming, where participants simultaneously comprehend auditory distractors (auditory [f1]; tagged at 54 Hz) while preparing to name related or unrelated target pictures (visual [f2]; tagged at 68 Hz). RIFT elicits steady-state evoked potentials, which reflect allocation of attention to the tagged stimuli. When representations of the tagged stimuli interact, increased power has been observed at the intermodulation frequency resulting from an interaction of the base frequencies (f2 ± f1; Drijvers et al., 2021). Our results showed clear power increases at 54 Hz and 68 Hz during the tagging window, but no power difference between the related and unrelated condition. Interestingly, we observed a larger power difference in the intermodulation frequency (compared to baseline) in the unrelated compared to the related condition (68 Hz–54 Hz: 14 Hz), indicating stronger interaction between unrelated auditory and visual representations. Our results go beyond standard PWI results by showing that participants’ difficulties in the related condition do not arise from allocating attention to the pictures or distractors. Instead, processing difficulties arise during interaction of the concepts or lemmas invoked by the two stimuli, thus, we conclude, that interaction might be downregulated in the related condition.