Symbolic task planning is a widely used approach to enforce robot autonomy due to its ease of understanding and deployment in robot architectures. However, techniques for symbolic task planning are difficult to scale in real-world, human-robot collaboration scenarios because of the poor performance in complex planning domains or when frequent re-planning is needed. We present a framework, Teriyaki, specifically aimed at bridging the gap between symbolic task planning and machine learning approaches. The rationale is training Large Language Models (LLMs), namely GPT-3, into a neurosymbolic task planner compatible with the Planning Domain Definition Language (PDDL), and then leveraging its generative capabilities to overcome a number of limitations inherent to symbolic task planners. Potential benefits include (i) a better scalability in so far as the planning domain complexity increases, since LLMs' response time linearly scales with the combined length of the input and the output, and (ii) the ability to synthesize a plan action-by-action instead of end-to-end, making each action available for execution as soon as it is generated instead of waiting for the whole plan to be available, which in turn enables concurrent planning and execution. Recently, significant efforts have been devoted by the research community to evaluate the cognitive capabilities of LLMs, with alternate successes. Instead, with Teriyaki we aim to provide an overall planning performance comparable to traditional planners in specific planning domains, while leveraging LLMs capabilities to build a look-ahead predictive planning model. Preliminary results in selected domains show that our method can: (i) solve 95.5% of problems in a test data set of 1,000 samples; (ii) produce plans up to 13.5% shorter than a traditional symbolic planner; (iii) reduce average overall waiting times for a plan availability by up to 61.4%