As Greece enters a new week with no imminent signs of securing a deal with creditors to unlock much-needed aid, talk that a debt default is "inevitable" has grown.

News emerged on Monday that Greece came so close to defaulting on a 750-million-euro ($855-million) repayment to the International Monetary Fund (IMF) last week that Greek Prime Minister, Alexis Tsipras, warned that the repayment could not be made without help from the European Union. Concerns that IMF debt will not be repaid sparked a sell-off in Greek bonds, with the yield on two-year bonds surged more than 250 basis points to 23.68 percent. Read More Just how is broke Greece paying its bills "A default event by Greece is inevitable," Carl B. Weinberg, chief economist at High Frequency Economics, wrote in a note published Monday. Euro zone governments are willing to lend Athens cash but only in return for strict reforms such as pension cuts, which the anti-austerity government says is a "red-line" that cannot be crossed. The stalemate has dragged on for weeks, hurting the country's economy, business sentiment and raising the prospect of a debt default and Greece's possible withdrawal from the single currency club.

The European Commission said on Monday while there was progress in talks between Greece and its creditors, the pace was slow and more effort was needed to secure agreement. "The only way this can end is that Greece will run out of cash," Weinberg added. "Neither side seems prepared to turn." Greece has relied on cash from the European Union and IMF to pay its bills since 2010. Current negotiations focus on unlocking the last tranche of aid, worth 7.2 billion euros, before a deadline expires at the end of June. And with further loan repayments due to the IMF next month, as well as the need for cash to pay pensions and wages, the clock is ticking for Athens.

Under pressure

Germany meanwhile maintained pressure on Greece to adopt reforms, with Economy Minister Sigmar Gabriel warning that further aid would be unlikely unless Greece made some changes, Reuters reported on Monday. "It (a default event) is on the cards, it's been on the cards for ages but the key is this: Greece is like a horse with three broken legs. The only discussion is about who is going to shoot it," Philippa Malmgren, founder of consultancy DRPM Group, told CNBC Europe's "Squawk Box" Monday. Read MoreThis may be a greater risk for Greece than default

"The Germans don't want to be seen pulling the trigger on this. Greece could commit suicide in a number of ways -- they could go back to the electorate; so this issue of elections comes back on the table. They could announce they are broke but governments usually don't like to do this." In recent weeks, talk of a referendum in Greece has emerged, although the idea has been ruled out by Tsipras. Analysts said that allowing the electorate to make the decision on further austerity in return for aid would take political pressure off a government elected on an anti-austerity mandate.

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