Novel configurations of superconducting magnets for helical muon beam cooling channels and demonstration experiments are being designed at Fermilab. The magnet system for helical cooling channels has to generate longitudinal solenoidal and transverse helical dipole and helical quadrupole fields. It was found that this complicated field configuration can be made by a helical solenoid, which is a set of circular coils shifted in transverse directions in such a way that their centers lay on the center of the helical beam orbit. This paper discusses the possibility of combining two such channels in one mechanical structure to allow beams of positive and negative muons to be cooled at the same time. The status of a short model helical solenoid prototype to study its magnetic and mechanical properties is also described.