Cellular communications are evolving to facilitate the current and expected increasing needs of quality of service, high data rates, and diversity of offered services. Toward this direction, radio access network (RAN) virtualization aims at providing solutions of mapping virtual network elements onto radio resources of the existing physical network. This paper proposes the Resources nEgotiation for NEtwork Virtualization (RENEV) algorithm, which is suitable for application in heterogeneous networks in Long-Term Evolution Advanced (LTE-A) environments, consisting of a macro evolved Node B overlaid with small cells (SCs). By exploiting radio resource management principles, RENEV achieves slicing and on-demand delivery of resources. Leveraging the multitenancy approach, radio resources are transferred in terms of physical radio resource blocks among multiple heterogeneous base stations, which are interconnected via the X2 interface. The main target is to deal with traffic variations in geographical dimension. All signaling design considerations under the current Third-Generation Partnership Project LTE-A architecture are also investigated. Analytical studies and simulation experiments are conducted to evaluate RENEV in terms of the network's throughput and additional signaling overhead. Moreover, we show that RENEV can be applied independently on top of already proposed schemes for RAN virtualization to improve their performance. The results indicate that significant advantages are achieved both from the network's and users' perspective and that it is a scalable solution for different numbers of SCs.