EU data protection rules could be difficult for researchers to navigate, particularly when processing massive datasets containing personal data for Artificial Intelligence (AI) developments. This article examines how data protection intersects with AI research to elucidate the issues arising from the use of large-scale databases containing personal data to train, test and validate AI systems. The key objectives of this work are to (1) scrutinise the data protection requirements and limits for the processing of personal data in AI research, (2) reflect on possible complications regarding data quality requirements for trustworthy AI and General Data Protection Regulation (GDPR) compliance, and (3) present possible ways forward to reconcile GDPR requirements and AI research. While reviewing and mapping relevant provisions and guidance, we identify data protection challenges posed by the use of massive databases containing personal data for AI research. The findings suggest that, while the legal regime for research under the GDPR resolves some of the challenges identified, others, such as legal basis for processing and processing of special categories of data, remain unaddressed. We argue that the nature of these complications will make it difficult for EU researchers to advance in trustworthy AI efforts. The analysis concludes by suggesting possible ways to tackle the remaining issues.