We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time, but it cannot prevent <?format ?>the formation of a singular point. However, the nature of the singularity depends on the value of . In the radiation case, a trapped surface is formed for , whereas for , a naked singularity is developed. In general, the critical value is , where is the parameter describing the equation of state of the fluid component.