Prioritizing the management of invasive alien species (IAS) is of global importance and within Europe integral to the EU IAS regulation. To prioritize management effectively, the risks posed by IAS need to be assessed, but so too does the feasibility of their management. While the risk of IAS to the EU has been assessed, the feasibility of management has not. We assessed the feasibility of eradicating 60 new (not yet established) and 35 emerging (established with limited distribution) species that pose a threat to the EU, as identified by horizon scanning. The assessment was carried out by 34 experts in invasion management from across Europe, applying the Non‐Native Risk Management scheme to defined invasion scenarios and eradication strategies for each species, assessing the feasibility of eradication using seven key risk management criteria. Management priorities were identified by combining scores for risk (derived from horizon scanning) and feasibility of eradication. The results show eradication feasibility score and risk score were not correlated, indicating that risk management criteria evaluate different information than risk assessment. In all, 17 new species were identified as particularly high priorities for eradication should they establish in the future, whereas 14 emerging species were identified as priorities for eradication now. A number of species considered highest priority for eradication were terrestrial vertebrates, a group that has been the focus of a number of eradication attempts in Europe. However, eradication priorities also included a diverse range of other taxa (plants, invertebrates and fish) suggesting there is scope to broaden the taxonomic range of attempted eradication in Europe. We demonstrate that broad scale structured assessments of management feasibility can help prioritize IAS for management. Such frameworks are needed to support evidence‐based decision‐making.