"We are ready to help Greece survive its economic crisis with cooperation in tourism, energy, trade," Turkish Prime Minister Ahmet Davutoglu said in the capital, Ankara.
"We want Greece to be strong... Therefore Turkey will be positive toward any proposal for cooperation," he said in televised comments.
Davutoglu added that a Turkish delegation would travel to Greece for a high-level cooperation meeting as soon as possible to consider joint steps on the financial crisis.
If no deal is reached, Greece is set to default on an IMF debt payment of about 1.5 billion euros ($1.7 billion) due Tuesday, risking an exit from the eurozone and even the European Union.
On Tuesday Greek Finance Minister Yanis Varoufakis said Athens will not make the IMF payment.
Greek Prime Minister Alexis Tsipras asked for Greece's bailout programme be extended for one month to allow a referendum on austerity demanded by Athens' creditors to be carried out Sunday, but his request was swiftly rejected by eurozone leaders.
Turkish Economy Minister Nihat Zeybekci said on Monday if an official proposal for financial aid is made by Greece, "we will evaluate it."
Turkey's left-wing and Pro-Kurdish Peoples' Democratic Party (HDP) also issued a message of solidarity with Greece, saying: "We are together with the Greek people and their government in their struggle for justice, equality and democracy and against austerity."
"We believe that apart from imposing austerity policies on peoples of Europe, there can be more reasonable agreements, which will be acceptable," said the co-chairs of HDP, considered the Turkish equivalent of Greece's ruling Syriza party.
Relations between Greece and Turkey have improved in recent years, but the continued division of Cyprus hinders closer ties between the two Aegean neighbours.
Cyprus has been divided since Turkey invaded the north on July 20, 1974, after a Greek Cypriot coup engineered by the junta then ruling Athens aimed at uniting the island with Greece.
Cyprus has also been a major stumbling block in Ankara's lagging negotiations to join the European Union.