Government have this morning issued a statement in which it confirms that the Sovereignty of Gibraltar is not a matter for discussion.

"Gibraltar and the United Kingdom continue to work closely together as we prepare to leave the European Union. The longstanding position of Her Majesty's Government of Gibraltar is that it remains ready to engage in technical discussions with all interested parties, including Spain, in this regard. The sovereignty of Gibraltar is not a matter for discussion.
The joint management of the air terminal, on a purely commercial basis, between Gibraltar and Spanish business interests was provided for in the agreement signed at Cordoba in 2006 between the then Governments  of Gibraltar, the United Kingdom and Spain.
This did not happen because Spain has not yet given effect to this and other relevant parts of the agreement."
The relevant clause in the 2006 Cordoba Agreement on Gibraltar Airport reads as follows:
All passenger and flight services including all facilities and functions relating to airside and aircraft services, passengers’ check-in, baggage handling and passenger and baggage security will be provided in and by the terminal. Subject to EU directives, the Government of Gibraltar will grant a contractual concession to operate the terminal and provide these services on a commercial basis to a joint venture company owned by Gibraltar and Spanish commercial interests.