MOTIVATION: The process of placing new drugs into the market is time-consuming, expensive and complex. The application of computational methods for designing molecules with bespoke properties can contribute to saving resources throughout this process. However, the fundamental properties to be optimized are often not considered or conflicting with each other. In this work, we propose a novel approach to consider both the biological property and the bioavailability of compounds through a deep reinforcement learning framework for the targeted generation of compounds. We aim to obtain a promising set of selective compounds for the adenosine A2A receptor and, simultaneously, that have the necessary properties in terms of solubility and permeability across the blood-brain barrier to reach the site of action. The cornerstone of the framework is based on a recurrent neural network architecture, the Generator. It seeks to learn the building rules of valid molecules to sample new compounds further. Also, two Predictors are trained to estimate the properties of interest of the new molecules. Finally, the fine-tuning of the Generator was performed with reinforcement learning, integrated with multi-objective optimization and exploratory techniques to ensure that the Generator is adequately biased. RESULTS: The biased Generator can generate an interesting set of molecules, with approximately 85% having the two fundamental properties biased as desired. Thus, this approach has transformed a general molecule generator into a model focused on optimizing specific objectives. Furthermore, the molecules' synthesizability and drug-likeness demonstrate the potential applicability of the de novo drug design in medicinal chemistry. AVAILABILITY AND IMPLEMENTATION: All code is publicly available in the https://github.com/larngroup/De-Novo-Drug-Design. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.