A mode cleaner optical cavity is a resonator that can be tuned to transmit a desired transverse mode present in the incoming beam, suppressing all the others. We present the optical design of a suited input mode cleaner for a small-scale Michelson interferometer, called SIPS (Suspended Interferometer for Ponderomotive Squeezing). The physical goal is to feed SIPS with a beam with a Gaussian profile, which also ensures a highly focused beam along the propagation axis. The SIPS mode cleaner has been designed to have a maximum circulating power of 130W, and to deliver a transmitted power of at least 2.5W in input of SIPS interferometer. It guarantees a suppression factor of at least 20 dB for every tested higher order mode. This work is framed within the implementation of a table-top optical experiment to test the broadband Quantum Noise reduction in the SIPS sensitivity curve, via frequency-dependent squeezing achieved by employing Einstein-Podolsky-Rosen quantum entangled states of light.