The problem of verifying the absence of collision between a cable and the mobile part(s) of a device located on-board the mobile platform of a Cable-Driven Parallel Robot (CDPR) is addressed. The set of all positions taken by one cable of the CDPR for all the poses of the mobile platform in a prescribed workspace is called the cable span. A simple bounding volume approximation of the cable span is proposed in this paper. This bounding volume is a polyhedron and the characterization of the faces of this polyhedron is discussed. Using this polyhedron as a bounding volume of the cable span allows to accelerate computations related to collision avoidance checking.