Can NRI deposit old Rs 500 and Rs 1000 notes into NRE/NRO Account?

One of the frequently asked question by NRI who are traveling to India or currently in India is that whether they can deposit their Rs 500 and Rs 1000 notes in their NRE account or not? Some of them have withdrawn the cash from their NRE account itself prior to the surprise declaration of demonetization by the prime minister on the night of 8th November.