Integrase is a key protein during HIV-1 replication as it catalyzes the integration of viral DNA into the host DNA. After several decades of research, highly potent and selective active site inhibitors have emerged. The new challenge is now to develop molecules with an original mode of action, targeting integrase out of its catalytic site. During a previous study, we developed an in vitro assay to monitor the interaction between HIV-1 integrase and one of its cellular partners, GCN2. This AlphaLISA-based assay was validated as a platform for chemical modulator screening. In the present study, we used a library of natural products from the Developmental Therapeutics Program (NIH) to identify novel chemical leads. The best modulators were characterized and a structure–activity relationship study was initiated with a limited number of derivatives. We found that most inhibitors were tricylic or tetraclyclic molecules, with the most potent belonging to the anthracyclines/anthraquinones. Of note, several molecules exhibited interesting cellular activities and may be suitable for further optimization.