Wake up from deep sleep on BLE interrupt

From what I understand bluetooth low energy is able to be in standby while using very low energy. This is very useful but its energy saving are negated by the fact that the board needs to be on to supply power and receive data to and from the module. I am wondering if there is a way I can put the board in deep sleep while supplying power to the Bluetooth module. Then when the Bluetooth module receives a signal it sends a signal to the board waking it up. Is this possible? If not is there some similar low power alternative. Keep in mind that this board will have other sensors attached to it but these can all be turned off when in deep sleep mode. The only thing that needs to stay on is the Bluetooth module and the RTC.