We theoretically and numerically study the design of optical "lumped" nanofiltering devices in the framework of our recently proposed paradigm for optical nanocircuits. In particular, we present a design of basic filtering elements, such as low-pass, pass-band, stop-band, and high-pass lumped nanofilters, for use in optical nanocircuits together with more complex designs, such as multizero or multipole nanofilters, to work at THz, infrared, and optical frequencies. Following the nanocircuit theory, we show how it is possible to design such complex frequency responses by applying simple rules, similar to those in rf circuit design, and we compare the frequency response of these optical nanofilters with classic filters in rf circuits. These findings introduce a theoretical foundation for the fabrication of nanofilters in optical lumped nanocircuit devices.