In one embodiment, a processor includes a core to execute instructions and a core perimeter logic coupled to the core. The core perimeter logic may include a fabric interface logic coupled to the core. In turn, the fabric interface logic may include a first storage to store state information of the core when the core is in a low power state, and enable an inter-die interconnect coupled between the core and an uncore to be maintained in an active state during entry of the core into a low power state. Other embodiments are described and claimed.