I understand until 2007 that the UK were in constant dialogue with Argentina about various issues relating to the Falkland Island including the sharing of Hydocarbon development.
Argentina says it wants "negotiate" , if that is so, it needs to first set out what it wants the acheive from the negotiations. What we aleady know is to CK "negotiate" means, "Send us the keys and turn the lights out when you leave".
This is written into the Argentine constitution, in other words, any Argentine President is bound to aim for this, and any real negotiation which led to anything less than full possession would be seen as a betrayal by the Argentine people.