This article attempts to clarify Francisco Varela's proposal of a neurophenomenology of time consciousness in the light of distinctions based on the philosophical literature of phenomenology and recent advances of neurobiology. The analysis is carried out considering three aspects. In the first of them, we discuss the phenomenological aspect of consciousness, accessible in first-person, which describes time as a structure with three inseparable moments (past-present-future) and three levels of temporality, and not merely as the chronometric time or clock time. In the second one, we analyze the neurobiological aspect of consciousness that tends to "explain" the phenomenological time in terms of three possible levels of neuronal integration. Thus, we propose a correspondence between the levels of phenomenological time and neural integration processes. Finally, we try to analyze this "correspondence" and the issues that follow from this by considering that the notion of time in this correspondence is, in essence, the clock time and not the phenomenological time consciousness.