The tiny rocky outcrop on Spain's southern tip has long been the subject of an acrimonious sovereignty row between London and Madrid, which wants Gibraltar back after it was ceded to Britain in 1713.
Since Britain's shock June vote to leave the European Union, Madrid has upped its rhetoric, arguing that Gibraltar should come back under the Spanish fold to continue enjoying much-needed EU benefits.
Gibraltar's flourishing economy, which is based on the financial services sector, tourism and online gaming, depends in large part on its access to the EU's single market.
"Spain has formally invited the United Kingdom to open negotiations to reach an agreement so that the mandates of European Union treaties keep being applied in Gibraltar," Spain's UN ambassador Roman Oyarzun told a committee on Tuesday, according to a copy of his speech.
He proposed joint sovereignty "which would allow Gibraltar to remain in the EU."
Under the plan, Gibraltarians would be able to keep their British nationality, and would also be able to gain Spanish citizenship.
The idea of joint sovereignty is not new, and such a proposal was etched out between Britain and Spain in 2001 and 2002. But it was binned after Gibraltarians rejected it in a November 2002 referendum.
In the committee meeting, Gibraltar's chief Fabian Picardo rejected the proposal outright, pointing to past rows between Spain and the Rock that affected its crucial land border, which many Spaniards cross every day to work in the British territory.
In a 2013 row over disputed waters, for instance, Spain upped border checks, creating hours-long logjams and forcing the European Commission to wade in and ease the crisis.
Gibraltar now fears that it will be at the mercy of Madrid without the protection of the EU.
"When it comes to the question of whether we will transfer all or any part of our sovereignty to Spain our answer will never change," Picardo said.
"It is simple: 'no way, Jose!'. You will never get your hands on our Rock. Never."
Peter Wilson, the UK's Deputy Permanent Representative at the UN, said Britain would not enter any negotiations with which Gibraltar was not content.
"The United Kingdom's vote to leave the European Union does not change our unwavering commitment to respecting Gibraltar's wishes on sovereignty," Mr Wilson told the Fourth Committee.
"As I have already said, we will not enter into arrangements under which the people of Gibraltar would pass under the sovereignty of another State against their freely and democratically expressed wishes."
"Nor will the United Kingdom enter into a process of sovereignty negotiations with which Gibraltar is not content," he said.