The search for compounds that can inhibit the interaction of certain viral proteins with their cellular partners is a promising trend in the development of antiviral drugs. We have previously shown that binding of HIV-1 integrase with human Ku70 protein is essential for viral replication. Here, we present a novel, cheap, and fast assay to search for inhibitors of these proteins’ binding based on the usage of genetically encoded fluorescent tags linked to both integrase and Ku70. Using this approach, we have elucidated structure-activity relationships for a set of oligonucleotide conjugates with eosin and shown that their inhibitory activity is primarily achieved through interactions between the conjugate nucleic bases and integrase. Molecular modeling of HIV-1 integrase in complex with the conjugates suggests that they can shield E212/L213 residues in integrase, which are crucial for its efficient binding to Ku70, in a length-dependent manner. Using the developed system, we have found the 11-mer phosphorothioate bearing 3’-end eosin-Y to be the most efficient inhibitor among the tested conjugates.