Nanofibers are very promising new type of material with a broad range of possible applications. The new NANOSPIDER technology opens a possibility to produce nanofabrics in an amount large enough for them to start being interesting as a construction material. There are many so-called passive applications of nanotextiles (including different types of filters and protective layers), and active applications, when the active chemical agent is incorporated in their structure. In the present paper, however, the new possible application of nanofabrics is proposed: as a base material on which technically interesting nanoclusters are heterogeneously nucleated. The basic thermodynamics of heterogeneous nucleation on nanofibers is considered. The extreme curvature of nanofibers manifests itself in an energetic barrier of nucleation, which is quite different from a case of nucleation on a flat surface. The expression for Gibbs energy of cluster formation is derived, taking into account the elastic strain resulting from a volume (or shape) changes during nucleation.