Yet there are some major obstacles that have to be overcome before any such talks occur. Foremost would be what to do with one of the island's eeriest monuments to inter-communal violence - the ghost city of Varosha.
Once a tourist destination rivalling Spain's Marbella and Majorca, this southern part of the ancient port city of Famagusta has been a virtual ghost town since 1974.
About 15,000 largely Greek Cypriot inhabitants fled after Turkish troops invaded the island - an attack launched in response to a coup attempt by Greek nationalists aiming to adjoin the island to Greece.
Turkish forces occupied Varosha, but then withdrew, putting up a ring of barbed wire and barricades around it. For 32 years, it has stood empty, save for the odd Turkish guard post, group of sunbathing officers and stray cat.
Prodromos Papavassilou, who was born and raised in the town, says he remembers it "every minute, every hour and every day". Now, along with many thousands of other former residents, he lives in the largely Greek Cypriot south of the island.
"It was the richest and one of the most beautiful towns of the island," he says, "with the best beach, pure golden sands with shallow waters."
Varosha is in the south of the
ancient port city of Famagusta
Metin Sahinoglu, the Turkish Cypriot manager of the Palm Beach hotel, one of the few hotels in Famagusta from before 1974 still operating, agrees.
"In my childhood, it was a city that never slept. There were streets of bars, restaurants, clubs – it was the liveliest place on the island."
From the Palm Beach hotel, which lies in the Turkish Cypriot north of the island, one of the Eastern Mediterranean's greatest beaches curves south in a series of ever-widening arcs. Yet walk 100 metres from the luxury hotel terrace and barbed wire cuts across the rows of sunshades and lounge chairs.
South of this twisted metal line stand dozens of skyscrapers and seafront hotels, stretching as far as the eye can see. This is Centre Beach, once famous for its hordes of German and British tourists during the summer months. Now, its kilometres of exclusive waterfront are empty and abandoned.
And behind the rusted barbed wire and oil drums that wall off the suburb, the dead streets are overgrown with fantastically unkempt trees, cactus and bougainvillea.
Old Greek street names poke through the shadows on bullet scared walls. Cars from the 1970s lie where they were abandoned after city residents took flight for fear of a massacre in July 1974.
"They felt no one would protect them," recalls Yiannakis Skordis, the Famagustan mayor-in-exile of Varosha who lives in Limassol, in the Greek Cypriot south.
"It was the richest and one of the most beautiful towns of the island, with the best beach, pure golden sands with shallow waters"
born and raised in Varosha
"The only thing they could do was run. Around Famagusta were many orange groves, so the population hid in those, but the bombs kept falling. They still all thought they would be going back to their homes in 10 days, though."
Today, many thousands of former residents remain on the island, scattered among other Greek Cypriot communities – still waiting to go back.
"I used to have nightmares for many years about going back there, imagining the devastation I would find," says Skordis, "Many of the buildings there were from the 19th century and were so beautiful.
"Every morning too, Centre Beach was cleaned and the streets washed with water. The best musicians and artists on Cyprus and from Europe and the Levant would go there. We loved our city. It was 20 years ahead of its time, ahead of the rest of the island."
But the city's fate has since lain in the lengthy debate between Turkish and Greek Cypriot leaders.
"It's said by many people that the Turkish side has kept the city closed as a bargaining chip with the Greek Cypriots," says Tim Potier, an assistant professor of law and human rights at Nicosia's Intercollege.
The invading Turkish army put up
barbed wire and barricades
"If the Greeks give them something, they can have the city back. But so far, the Greek Cypriots have refused to take the bait."
The Turkish invasion of 1974 led to the de facto division of the island between a Turkish Cypriot north and a Greek Cypriot south.
Only the Greek Cypriot dominated southern Republic of Cyprus is internationally recognised. The Turkish Cypriots are supported only by neighbouring Turkey.
Since 1974 too, an international economic embargo against the Turkish Cypriots has been in place. As a result, the port of Famagusta – the best on the island – has become neglected, serving only Turkish freighters.
Reopen the port
Yet trade had long been Famagusta's bread and butter. During medieval times, it was one of the richest cities on earth, thanks to its location as a frontier post between Christian Europe and the Muslim Middle East.
"Famagusta has 37 centuries of history," says Skordis. "We have proposed that some joint Turkish-Greek Cypriot company could be set up, under European Union or United Nations regulation, to reopen the port. It would give us a great opportunity to start the process of bringing us back together."
However, such schemes have gone nowhere in the heated disputes over the island's future.
Cars in Varosha lay rusting where
they were in 1974
"We Turkish Cypriots have long shown our willingness to reopen Varosha," says Sahinoglu. "We were very hopeful too a couple of years ago this would happen."
Then, a UN plan to reunite the island and take down the barbed wire was put to a referendum in both Cypriot communities. But the Greek Cypriots rejected the plan almost as strongly as the Turkish Cypriots accepted it.
"There's no willingness to share, that we can see," continues Sahinoglu. There's no light at the end of this tunnel."
Back at the line of tattered oil drums that cuts across what was once a major boulevard, dusk is falling. A battered Coca-Cola sign creaks slowly in the slight breeze above the permanently shuttered Agamemnon Cafe.
"Sometimes, at night, it's very scary living here," says Ahmet Ustuoglu, a Turk from the mainland who, in the late 1970s, like many others, settled with his family in an abandoned Greek Cypriot house next to the fenced-off phantom city.
"You look across there and you know there are streets and houses and apartment blocks, and cinemas and restaurants and shops – but there are no lights. Not one. It is like the end of the world, just there, across the street from you."
And the ghost city looks likely to cast its shadow over the island for some time to come, as the two sides continue to argue over its future.
Pictures by Jody Sabral