A UN-administered boundary currently separates Cyprus
Britain is "formally renewing" an offer to hand over half of its sovereign territory in Cyprus to facilitate a peace deal, the United Nations says.
Britain controls 3% of territory on Cyprus, which was a UK colony until 1960 and has since seen conflict between Greek and Turkish Cypriots.
The renewal of the offer came as the Cypriot president Demetris Christofias arrived on a visit to London.
Downing Street said it would issue a statement after he met Gordon Brown.
"The offer would be conditional on a comprehensive agreement being agreed by the leaders of the two communities and then accepted by a majority of their populations and formally ratified by both sides," the UN said in a statement.
Cyprus was split in a Turkish invasion in 1974 which was triggered by a brief Greek-inspired coup.
The Greek and Turkish Cypriot sides re-started peace negotiations in September 2008.
The offer would be for a handover of 45 square miles, just under half of the 98 square miles (254 sq km) that Britain now controls.
BBC world affairs correspondent Mike Wooldridge said the British government first made its conditional offer in 2003, before modifying it in 2004. The same offer has now been repeated.
There are two British bases in the British sovereign territory.
It is understood they would both continue in operation after the handing over of the territory.
The Greek and Turkish Cypriots restarted peace negotiations in September last year, and it is understood that the British government hopes that renewing this offer now could give "a bit of a boost to a process that seems to lack movement".
The Turkish Cypriot leader since 2005, Mehmet Ali Talat, favours reunification and membership of the EU for the whole island but he will soon be facing a new election.
The National Unity Party, which favours unification with Turkey, won parliamentary elections in the Turkish-held area in April of this year.