Faymann, who is visiting Greece on Tuesday and has generally been sympathetic to Greece's arguments, told Greek state agency ANA that "Greece constitutes a warning on what happens when one applies only austerity."
The chancellor argued in favour of a five-year plan to "give hope back" to the Greeks.
While the European executive insisted on Monday that the EU-IMF creditors had made "major concessions", the radical left government in Athens continues to reject what it views as "irrational" austerity demands.
The talks concerning the release of the €7.2 billion ($8.1 billion) in rescue funds remaining in Greece's bailout have dragged on for five months.
On Monday, hours after Prime Minister Alexis Tsipras defiantly called on the creditors to be "more realistic," Athens said it was ready to return to the talks "at any time."
"We await the invitation of the (creditors) and will respond at any time to continue the negotiation," Tsipras' office said, although it did not say if it was ready to meet the creditors' demands.
But an EU spokeswoman said the EU and IMF have already made "major concessions" to Greece. "It's not a one-way street," Annika Breidthardt told a press conference.
She added: "The concessions ... made and the flexibility that has been shown are already quite substantial."
In Frankfurt, European Central Bank chief Mario Draghi urged all sides "to go the extra mile" but insisted the ball was in Athens' court.
"A strong and credible agreement with Greece is needed, not only in the interest of Greece, but also of the euro area as a whole," Draghi told the European Parliament's Committee on Economic and Monetary Affairs in Brussels.
"While all actors will now need to go the extra mile, the ball lies squarely in the camp of the Greek government to take the necessary steps," he said.
The deadlock sent the Athens Stock Exchange plunging as much as 7.14 percent Monday before closing with a 4.68 percent drop, with bank stocks especially hard hit.
Draghi however gave the assurance that the banks were currently solvent and that the ECB will continue to provide liquidity to them to help finance the economy.
Greece's €240 billion bailout expires on June 30th, and to meet that deadline, a reform deal must be resolved by a meeting in Luxembourg on Thursday of the eurozone's 19 finance ministers, who control the purse strings of the rescue programme.
Also at the end of the month, Greece faces a €1.6 billion payment to the IMF with another €6.7 billion due to the European Central Bank in July and August, which Greek officials have said the government cannot afford.
Its debt mountain is equivalent to 180 percent of GDP, or almost twice the country's annual economic output.