Neuraminidase (NA) of influenza viruses enables the virus to access the cell membrane. It degrades the sialic acid contained in extracellular mucin. Later, it is responsible for releasing newly formed virions from the membrane of infected cells. Both processes become key functions within the viral cycle. Therefore, it is a therapeutic target for research of the new antiviral agents. Structure–activity relationships studies have revealed which are the important functional groups for the receptor–ligand interaction. Influenza virus type A NA activity was inhibited by five scaffolds without structural resemblance to sialic acid. Intending small organic compound repositioning along with drug repurposing, this study combined in silico simulations of ligand docking into the known binding site of NA, along with in vitro bioassays. The five proposed scaffolds are N-acetylphenylalanylmethionine, propanoic 3-[(2,5-dimethylphenyl) carbamoyl]-2-(piperazin-1-yl) acid, 3-(propylaminosulfonyl)-4-chlorobenzoic acid, ascorbic acid (vitamin C), and 4-(dipropylsulfamoyl) benzoic acid (probenecid). Their half maximal inhibitory concentration (IC50) was determined through fluorometry. An acidic reagent 2′-O-(4-methylumbelliferyl)-α-dN-acetylneuraminic acid (MUNANA) was used as substrate for viruses of human influenza H1N1 or avian influenza H5N2. Inhibition was observed in millimolar ranges in a concentration-dependent manner. The IC50 values of the five proposed scaffolds ranged from 6.4 to 73 mM. The values reflect a significant affinity difference with respect to the reference drug zanamivir (p < 0.001). Two compounds (N-acetyl dipeptide and 4-substituted benzoic acid) clearly showed competitive mechanisms, whereas ascorbic acid reflected non-competitive kinetics. The five small organic molecules constitute five different scaffolds with moderate NA affinities. They are proposed as lead compounds for developing new NA inhibitors which are not analogous to sialic acid.