This paper is a first step towards identifying the links between the characteristics of gaze behaviour and visitor preferences in a museum. In the long term, the real-time analysis of visitors' gaze should allow a fine estimation of their interest for the different artworks exhibited and should replace the fastidious and time-consuming elicitation of preferences commonly used in traditional recommender systems. To study these links, we carried out a user study at the Nancy Museum of Fine Arts in the North-East of France. This pilot study involved 13 volunteers who had the opportunity to freely explore the museum and contemplate hundreds of artworks for more than 50 minutes on average in May 2018. We were able to analyze millions of fixation points so as to find correlations between the number of fixation points per painting, the time spent looking at a painting, and whether or not this painting is appreciated. We plan to extend this study to 100 visitors in the coming months.