Theories of conversation propose that in order to have smooth transitions from one turn to the next, speakers already plan their response while listening to their interlocutor. Moreover, it has been argued that speakers align their linguistic representations (i.e. prime each other), thereby reducing the processing costs associated with concurrent listening and speaking. In two experiments, we assessed how identity and associative priming from spoken words onto picture naming were affected by a concurrent speech planning task. In a baseline (no name) condition, participants heard prime words that were identical, associatively related, or unrelated to target pictures presented two seconds after prime onset. Each prime was accompanied by a non-target picture and followed by its recorded name. The participant did not name the non-target picture. In the plan condition, the participants first named the non-target picture, instead of listening to the recording, and then the target. In Experiment 1, where the plan- and no-plan conditions were tested between participants, priming effects of equal strength were found in the plan and no-plan condition. In Experiment 2, where the two conditions were tested within participants, the identity priming effect was maintained, but the associative priming effect was only seen in the no-plan but not in the plan condition. In this experiment, participant had to decide at the onset of each trial whether or not to name the non-target picture, rendering the task more complex than in Experiment 1. These decision processes may have interfered with the processing of the primes. Thus, associative priming can take place during speech planning, but only if the cognitive load is not too high.