"We are hoping to hold a meeting at the beginning of next week... We are hoping for a meeting as soon as possible," Michel Bonnardeaux told AFP.
The Greek and Turkish Cypriots have now agreed on a road map prepared by the United Nations to resume talks on reunification of the island.
Efforts to relaunch the UN-brokered talks gathered pace this week after being deadlocked for nearly two years.
Both the Greek Cypriots and Turkish Cypriots have been working feverishly to finalise a joint declaration allowing them to restart the negotiations.
A resumption was further delayed by the eurozone debt crisis, which forced the Greek Cypriot government to secure a bailout from international creditors last March, plunging the island into deep recession.
But on Thursday, President Nicos Anastasiades said there were "serious prospects" of resuming talks with the Turkish Cypriots as the two sides were close to agreeing on a joint declaration.
Ozdil Nami, foreign minister of the breakaway self-declared Turkish Republic of Northern Cyprus, said efforts had been intensifying to reach a compromise.
Divided Cyprus joined the EU in 2004, after the failure of an accord to reunify it that was approved by the Turkish Cypriots but rejected by the Greek Cypriots.
Yesterday, Greece gave its backing to renewed talks, with Prime Minister Antonis Samaras calling them "one of the leading priorities of Greek foreign policy".
The two sides will "sit around the table and will be responsible for driving the negotiations towards a solution", Samaras said after talks with Anastasiades in Athens.
A draft joint statement leaked to the media says any final agreement would be subject to a referendum on each side of the dividing line.
The United States has also offered its support, and it is thought that pressure from Washington prompted the breakthrough.
Yesterday, Vice President Joe Biden expressed Washington's "unwavering support" for a Cyprus settlement and said he "looked forward to a successful resumption" of the talks, in a call with Anastasiades.
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