Antimicrobial resistance (AMR) is a current public health issue globally. To counter this phenomenon and prioritize AMR in the health sector, the World Health Organization (WHO) published a list of bacterial pathogens against which the development of new antimicrobial agents is urgently needed, designating the ESKAPE pathogens (i.e., Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacter species) with a ‘priority status’. Moreover, the One Health High Level Expert Panel (OHHLEP) states that human health is closely linked to animal and environmental health, thus promoting a holistic One Health approach in order to be prepared to address possible emerging health threats from the human–animal–environment interface. Wild birds may host and spread pathogens, integrating the epidemiology of infectious diseases. The aim of this study was to examine the role of wild birds as a source of ESKAPE bacteria and other antibiotic-resistant enterobacterales. A total of fifty strains within the ESKAPE group were detected in 40/163 cloacal samples of examined birds (24.5%). Additionally, different strains of enterobacterales were detected in 88/163 cloacal samples (53.9%). Isolated strains exhibited antimicrobial resistance, including towards critically important antibiotics (e.g., third, fourth, fifth generation cephalosporins, fluoroquinolones) for human medicine. Our results confirm that wild birds are potential reservoirs of several pathogens and antimicrobial-resistant bacteria and that they could be involved in the dissemination of those bacteria across different environments, with resulting public health concerns.