This is believed to be the first time that a Greek Cypriot leader has made such a move in wanting to directly negotiate with Turkey, a country that does not recognise Cyprus.
"I wish to disclose ... that we have sent a message to the government of our neighbouring country saying we are ready for dialogue to explain our positions," said Papadopoulos on Friday.
"And to say how we see the relations between Cyprus and Turkey developing before and after 17 December until Turkey's accession to the European Union, and how we see a common peaceful future as members of the Union," he added.
It was unclear where and at what level these negotiations would occur.
Turkey's EU candidacy could be blocked by member state Cyprus, which has not ruled out the veto card.
Turkey has occupied a third of
Cyprus since 1974
On 17 December, EU leaders will take a political decision on recommendations by the European Commission that accession negotiations with Turkey begin.
"In principle we are in favour of Turkey's candidacy ... because we are convinced that a truly European Turkey will be a factor of stability in our region and a secure link between Europe and the Middle East," said Papadopoulos.
However, this was conditioned on Turkey recognising the government of Cyprus as it does the governments of the other 24 member states, said the president.
Cyprus sees a unique opportunity to apply pressure to win concessions from Turkey, which has occupied one-third of the island since 1974, when Turkish troops invaded in response to an Athens-engineered coup to unite Cyprus with Greece.