The increasing demand for wireless broadband connectivity is leading mobile network operators towards new means to expand their infrastructures efficiently and without increasing the cost of operation. Network Functions Virtualization (NFV) is a step towards virtualization-based, low-cost flexible and adaptable networking services. In the context of centralized baseband architectures, virtualization is already employed to run baseband processing units as software on top of conventional data center hardware. However, current virtualization solutions consider atomic virtualization, i.e., single virtual machines implementing all baseband functionalities. In this article, we propose the fine-grained virtualization of baseband processing to achieve a more flexible distribution of the processing workload in centralized architectures. We also evaluate the benefits of our approach in terms of (i) the bandwidth requirements for each fine-grained distribution option, (ii) the latency experienced by mobile users for each fine-grained distribution option, and (iii) the total CPU usage of each fine-grained baseband processing function.