A new design for halloysite nanotube materials was obtained by grafting chemically modified cyclodextrin units onto the nanotube surface. In particular, grafted cyclodextrins were decorated with thiosaccharide pendants, in order to mimic the well-known binding of sugars to proteins and the glyco-cluster effect occurring during cellular recognition events. The obtained materials were characterized by using a combination of varied techniques (FT-IR spectroscopy, thermogravimetric analysis, scanning electron microscopy, dynamic light scattering, turbidimetry), and their potential drug-delivery abilities were tested by studying their interactions with the common naturally occurring anticancer agent curcumin. A suitable model describing the interaction between our materials and curcumin is proposed.