Although Charles is technically eligible for the title, it is however unlikely he would ever take it.
As Charles is heir to the throne, his role of Prince of Wales – and eventually, King – takes precedence over the Dukedom.
If Charles was given the title of Duke of Edinburgh, it would be merged with the Crown once again when he becomes King.
Therefore it makes sense the title would be returned to the Crown, to be distributed to another member of the Royal Family who is not directly in line to the throne.