Climate change and the related temperature rise can cause an increase in evapotranspiration. Thus, the assessment of potential evapotranspiration (PET) trends is important to identify possible ongoing signals of climate change, in order to develop adaptation measures for water resource management and improve irrigation efficiency. In this study, we capitalize on the data available from a network of 46 complete meteorological stations in Sicily that cover a period of about 21 years (2002–2022) to estimate PET by the Food and Agriculture Organization (FAO) using the Penman–Monteith method at the daily time scale in Sicily (southern Italy). We then analyse the trends of PET and assess their significance by Sen’s Slope and the Mann–Kendall test at multiple temporal scales (monthly, seasonal, and annual). Most of the locations do not show significant trends. For instance, at the annual timescale, only five locations have a significantly increasing trend. However, there are many locations where the monthly trend is statistically significant. The number of locations where monthly trend is significant is maximum for August, where 18 out of these 46 stations have an increasing trend. In contrast, in March, there are no locations with a significant trend. The location with the highest increasing trend of PET indicates trend slopes of 1.73, 3.42, and 10.68 mm/year at monthly (August), seasonal (summer), and annual timescales, respectively. In contrast, decreasing PET trends are present only at the monthly and seasonal scales, with a maximum of, respectively, −1.82 (July) and −3.28 (summer) mm/year. Overall, the findings of this study are useful for climate change adaptation strategies to be pursued in the region.