Sufficient supplies of critical raw materials (CRMs) for rapidly developing technologies, e.g., Li-ion batteries, wind turbines, photovoltaics, digitization, etc., have become one of the main economic challenges for the EU. Due to growing import dependency and associated risk of supply disruptions of these raw materials from third countries, there is a need to encourage their domestic production. This is an important starting point for EU value chains crucial for the sustainable economic growth of the whole Union. This contribution has evaluated the possibilities of CRMs supply from the EU’s primary sources. A three-step approach, including an assessment of CRMs’ importance for the EU’s economic growth, their significance in at least two of the three strategic industrial sectors (i.e., renewable energy, e-mobility, defense and aerospace), and their potential availability from EU mineral deposits, has been applied. Results of the analysis have shown that, of 29 critical mineral raw materials (according to the 2020 EC list), the potential to develop manufacturing from the Union mineral deposits exists for 11 CRMs, i.e., cobalt, graphite (natural), HREE, LREE, lithium, magnesium, niobium, PGMs, silicon metal, titanium, and tungsten, while some other CRMs, namely gallium, germanium, indium, and vanadium can be recovered as by-products. Measures to mitigate EU import dependency have been also proposed.