"We think this issue is open, we will proceed carefully," government spokesman Dimitris Tzanakopoulos told reporters.
He had been asked about speculation that Greek Prime Minister Alexis Tsipras was arranging to meet Turkish President Recep Tayyip Erdogan, reportedly on December 4.
Tzanakopoulos said that during a phonecall with Erdogan on Friday, Tsipras "expressed desire for a bilateral meeting" but added that no specific date had been set.
"After yesterday's (breakdown in talks) we will see what happens," the spokesman said.
The much-heralded talks in the Swiss resort of Mont Pelerin between Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci were supposed to produce a map of the internal boundaries of a future federation and pave the way for broader talks aimed at reaching a deal by early next year.
But like the five days of negotiations earlier in November, the two-day session broke up in the early hours of Tuesday without progress, and with each side blaming the other.
Cyprus has been divided since 1974, when Turkish troops invaded the northern third of the island in response to an Athens-inspired coup seeking union with Greece.
Owing to agreements that led to the island's independence in 1960, Britain, Greece and Turkey have guarantor powers in Cyprus.
The Greek Cypriots and Athens want to scrap this arrangement, while the Turkish Cypriots are reluctant to do so.
A Greek diplomatic source this week said Athens wants the guarantee issue resolved before it joins multi-party talks on Cyprus.
"Greece has agreed to join multi-party talks, provided there is a prior agreement between Greece and Turkey on the issue of guarantees and security," the source said.
"Greece will not join multi-party talks unless this discussion is held (first)."