In an embodiment, a processor includes a plurality of cores each to independently execute instructions, a cache memory including a plurality of portions distributed across a die of the processor, a plurality of sleep circuits each coupled to one of the portions of the cache memory, and at least one sleep control logic coupled to the cache memory portions to dynamically determine a sleep setting independently for each of the sleep circuits and to enable the corresponding sleep circuit to maintain the corresponding cache memory portion at a retention voltage. Other embodiments are described and claimed.