Antibiotic resistance is a global threat to public health, and the search for new antibacterial therapies is a current research priority. The aim of this in silico study was to test nine new fluoroquinolones previously designed with potential leishmanicidal activity against Campylobacter jejuni, Escherichia coli, Neisseria gonorrhoeae, Pseudomonas aeruginosa, and Salmonella typhi, all of which are considered by the World Health Organization to resistant pathogens of global concern, through molecular docking and molecular dynamics (MD) simulations using wild-type (WT) and mutant-type (MT) DNA gyrases as biological targets. Our results showed that compound 9FQ had the best binding energy with the active site of E. coli in both molecular docking and molecular dynamics simulations. Compound 9FQ interacted with residues of quinolone resistance-determining region (QRDR) in GyrA and GyrB chains, which are important to enzyme activity and through which it could block DNA replication. In addition to compound 9FQ, compound 1FQ also showed a good affinity for DNA gyrase. Thus, these newly designed molecules could have antibacterial activity against Gram-negative microorganisms. These findings represent a promising starting point for further investigation through in vitro assays, which can validate the hypothesis and potentially facilitate the development of novel antibiotic drugs.