Collaboration between start-ups and large companies can accelerate innovation and improve the performance of all actors involved. This study aims to analyse the factors that push innovative start-up entrepreneurs to enter into this type of alliance. To do this, we built a conceptual model based on the theory of planned behaviour (TPB). We used a quantitative method and collected data from a sample of 145 Italian startups. The model was then tested, using a partial-least squares approach to structural equation modelling (PLS-SEM). The results confirm the predictions of the TPB, namely that perceived behavioural control, subjective norm, and above all attitude, influence the intention of the start-uppers to collaborate with large companies. These results provide a twofold theoretical contribution by: 1) extending the TPB to the case under examination and 2) helping to explain the formation mechanisms of asymmetrical alliances between young innovative firms and large consolidated companies. This study further provides a practical contribution by indicating the levers that encourage the involvement of start-ups in open innovation programs and, at the same time, make entrepreneurs more aware of the mechanisms activated to involve them.