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Inspired by cognitive theories of creativity, this paper introduces a computational model (AIGenC) that lays down the necessary components to enable artificial agents to learn, use and generate transferable representations. Unlike machine representation learning, which relies exclusively on raw sensory data, biological representations incorporate relational and associative information that embeds rich and structured concept spaces. The AIGenC model poses a hierarchical graph architecture with various levels and types of representations procured by different components. The first component, Concept Processing, extracts objects and affordances from sensory input and encodes them into a concept space. The resulting representations are stored in a dual memory system and enriched with goal-directed and temporal information acquired through reinforcement learning, creating a higher-level of abstraction. Two additional components work in parallel to detect and recover relevant concepts and create new ones, respectively, in a process akin to cognitive Reflective Reasoning and Blending. The Reflective Reasoning unit detects and recovers from memory concepts relevant to the task by means of a matching process that calculates a similarity value between the current state and memory graph structures. Once the matching interaction ends, rewards and temporal information are added to the graph, building further abstractions. If the reflective reasoning processing fails to offer a suitable solution, a blending operation comes into place, creating new concepts by combining past information. We discuss the model's capability to yield better out-of-distribution generalisation in artificial agents, thus advancing toward Artificial General Intelligence.