Gibraltar is in talks with Scotland about various options to keep parts of the UK in the European Union.
Majorities in both Gibraltar and Scotland voted in favour of remaining in the EU as did Northern Ireland which could potentially be involved in the talks. More than 95% of Gibraltarians voted to stay in.
One possibility under discussion is for Gibraltar and Scotland to maintain the UK's membership of the bloc.
"I can imagine a situation where some parts of what is today the member state United Kingdom are stripped out and others remain," Gibraltar chief minister Fabian Picardo told Newsnight.
"That means that we don't have to apply again for access, we simply remain with the access we have today, and those parts that leave are then given a different sort of access, which is negotiated but not necessarily under Article 50," he said.
A precedent is the case of Denmark which joined the EEC in 1973. When Greenland gained autonomy from Denmark in 1979, it subsequently withdrew from the EU in 1985 as a result of a referendum.
Shortly after the UK referendum result was announced, Spain again expressed its interest in joint sovereignty of Gibraltar.
"The Spanish flag on the Rock is much closer than before," Spain's acting Foreign Minister Jose Manuel Garcia-Margallo said on Friday.
"Anybody who thinks that this is a time to propose joint sovereignty or that they're going to get any millimetre of advantage in respect of the sovereignty of Gibraltar is completely wrong. They shouldn't waste their breath, they shouldn't waste their time, they shouldn't waste the time of the European people as we try to navigate this issue that has been presented to us on Friday morning," Picardo retorted.
A 2002 referendum in Gibraltar rejected an earlier proposal of shared sovereignty.
On Saturday nuclear submarine HMS Ambush arrived in Gibraltar in what the UK navy said was a long planned visit but was viewed by some as sending a clear message to Madrid.
During the referendum campaign, Foreign Secretary Philip Hammond said it would be harder to protect Gibraltar if the UK left the EU.
“'We will be less able to protect Gibraltar's interests - not defend Gibraltar's territory, of course we can do that, but to protect Gibraltar's interests - if we are not inside the European Union,” he told ITV.
The Foreign Office has assured Gibraltarians that the UK will “continue to stand beside Gibraltar” and will never negotiate its sovereignty against the will of its people.
