Since the advent of Large Language Models (LLMs), much work has been devoted to comparing the linguistic abilities of humans and machines. Figurative language, which is known to rely on pragmatic inferential processes as well as lexical-semantic, sensorimotor, and socio-cognitive information, has been often used as a benchmark for this comparison. In the present study, we build on previous behavioral evidence showing that both distributional and sensorimotor variables come into play when people are asked to produce novel and apt metaphors and examine the behavior of LLMs in the same task. We show that, while distributional features still hold a special status, LLMs are insensitive to the sensorimotor aspects of words. This points to the lack of human-like experience-based grounding in LLMs trained on linguistic input only, while offering further support to the multimodality of conceptual knowledge involved in metaphor processes in humans.