Actually, no, or more precisely not yet.
The 1947 creation of the Dukedom of Edinburgh passes to the Prince Wales per the Letters Patent creating it.
When the Prince succeeds to the Throne, the Dukedom will “merge with the Crown” and will be available to be granted to the Earl of Wessex.
The only way this will not happen is if the Prince of Wales, Duke of Cambridge and Prince George were to all predecease the Queen. In that case, Princess Charlotte would become Queen and Prince Louis would inherit both the Edinburgh and Cambridge titles (among others).
or King Charles might decide to deny the title to his brother, or King William could deny his uncle when his father predeceases the Queen.