Electrical and electronic wastes (WEEEs) are a potential source of raw materials. The main challenge for scientists is to set up a reliable and eco-friendly process to recycle raw materials and precious elements from WEEEs. Today, we know that fungi could play an active role in green technologies aimed at recycling valuable elements. The bioaccumulation mechanism and bioleaching activity of filamentous fungal species have already been exploited fruitfully in extraction processes. However, not all fungal strains possess the same characteristics, and it is crucial to choose the right strains to use. In this work, we show a method to assess the precious elements’ recovery efficiency from WEEE using fungal strains. A CAS agar screening test for siderophore detection was carried out with three strains. The following plate accumulation test performed on a medium added with 120 ppm of electronic waste powder highlighted the differences in accumulation capability, growth rate, and biomass production. Among the elements in tested waste, yttrium, copper, and palladium show the highest bioconcentration factor. The results confirm the biotechnological potential of fungi to recover valuable elements at the bench scale, highlighting the importance of effective screening tests to assess the most efficient strain for each kind of waste.