The adsorption of viruses from aqueous solution is frequently performed to detect viruses. Charged filtration materials capture viruses via electrostatic interactions, but lack the specificity of biological virus-binding substances like heparin. Herein, we present three methods to immobilize heparin-mimicking, virus-binding polymers to a filter material. Two mussel-inspired approaches are used, based on dopamine or mussel-inspired dendritic polyglycerol, and post-functionalized with a block-copolymer consisting of linear polyglycerol sulfate and amino groups as anchor (lPGS-b-NH2). As third method, a polymer coating based on lPGS with benzophenone anchor groups is tested (lPGS-b-BPh). All three methods yield dense and stable coatings. A positively charged dye serves as a tool to quantitatively analyze the sulfate content on coated fleece. Especially lPGS-b-BPh is shown to be a dense polymer brush coating with about 0.1 polymer chains per nm². Proteins adsorb to the lPGS coated materials depending on their charge, as shown for lysozyme and human serum albumin. Finally, herpes simplex virus type 1 (HSV-1) and severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) can be removed from solution upon incubation with coated fleece materials by about 90% and 45%, respectively. In summary, the presented techniques may be a useful tool to collect viruses from aqueous environments.