Understanding how visual content communicates sentiment is critical in an era where online interaction is increasingly dominated by this kind of media on social platforms. However, this remains a challenging problem, as sentiment perception is closely tied to complex, scene-level semantics. In this paper, we propose an original framework, MLLMsent, to investigate the sentiment reasoning capabilities of Multimodal Large Language Models (MLLMs) through three perspectives: (1) using those MLLMs for direct sentiment classification from images; (2) associating them with pre-trained LLMs for sentiment analysis on automatically generated image descriptions; and (3) fine-tuning the LLMs on sentiment-labeled image descriptions. Experiments on a recent and established benchmark demonstrate that our proposal, particularly the fine-tuned approach, achieves state-of-the-art results outperforming Lexicon-, CNN-, and Transformer-based baselines by up to 30.9%, 64.8%, and 42.4%, respectively, across different levels of evaluators' agreement and sentiment polarity categories. Remarkably, in a cross-dataset test, without any training on these new data, our model still outperforms, by up to 8.26%, the best runner-up, which has been trained directly on them. These results highlight the potential of the proposed visual reasoning scheme for advancing affective computing, while also establishing new benchmarks for future research.