The problem of reverse engineering in the topology of functional interaction networks from time-course experimental data has received considerable attention in literature, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. The present work introduces a novel technique, CORE-Net, which addresses this problem focusing on the case of biological interaction networks. The method is based on the representation of the network in the form of a dynamical system and on an iterative convex optimisation procedure. A first advantage of the proposed approach is that it allows to exploit qualitative prior knowledge about the network interactions, of the same kind as typically available from biological literature and databases. A second novel contribution consists of exploiting the growth and preferential attachment mechanisms to improve the inference performances when dealing with networks which exhibit a scale-free topology. The technique is first assessed through numerical tests on in silico random networks, subsequently it is applied to reverse engineering a cell cycle regulatory subnetwork in Saccharomyces cerevisiae from experimental microarray data. These tests show that the combined exploitation of prior knowledge and preferential attachment significantly improves the predictions with respect to other approaches.