David Cameron will join fellow European Union leaders in Brussels for crisis meetings which could decide whether Greece has a future in the eurozone.
Finance ministers from the eurozone nations were locked in talks on Athens' proposals which offer austerity measures in exchange for a fresh bailout.
In an indication of the difficulties Greece will face in persuading its international creditors to extend an economic lifeline, the head of the eurozone's finance ministers warned there was a "major issue of trust" with the radical Syriza administration in Athens.
Greek prime minister Alexis Tsipras has offered to implement tax rises and spending cuts in return for a financial lifeline of 53.5 billion euro (£38.5 billion) to stave off bankruptcy and the possibility of crashing out of the euro.
But Dutch finance minister Jeroen Dijsselbloem, the eurogroup president, said a deal was still a long way off because there was concern that Greece would not meet its promises.
"There is, of course, a major issue of trust: can the Greek government actually be trusted to do what they are promising to actually implement in the coming weeks, months and years?" he told reporters as he arrived at the Brussels meeting.
That sentiment was echoed by German finance minister Wolfgang Schaeuble, one of the key players in the negotiations.
"We will definitely not be able to rely on promises," he said.
"We are determined to not make calculations that everyone knows one cannot believe in."
In Finland, there were reports that the coalition government was refusing to back further assistance for Greece.
In a sign of the increasingly desperate attempts to find a solution to the crisis, reports suggested that Germany was pushing the idea of a temporary five-year long Greek exit - Grexit - from the eurozone.
Theodoros Mihopoulos, who heads Mr Tsipras' office, said the report in Germany's Frankfurter Allgemeine Sonntagszeitung newspaper "is completely denied".
According to the report, the German finance ministry also proposed that the Greek government sells off some 50 billion euro (£36 billion) in unspecified property assets to pay off debts.
The report said that in exchange, Greece would remain in the EU and receive additional "growth enhancing, humanitarian and technical assistance".
With Greece running out of money, and facing a July 20 demand for a three billion euro (£2.16 billion) payment to the European Central Bank (ECB), this weekend's meetings in Brussels could hold the key to the country's economic future.
A meeting of the eurozone's leaders is scheduled for later today, followed by a full summit of the heads of government from all 28 EU member states.
Mr Cameron was urged by former Tory chancellor Lord Lawson to use the crisis to secure a more ambitious deal for the UK than the Prime Minister is currently hoping to achieve in his renegotiation.
The peer, writing in the Mail on Sunday, said Mr Cameron should be "championing the cause of Grexit" to show the EU that the goal of ever-closer union could not be imposed.
"It is clear the only hope for the long-suffering Greek people is to exit the eurozone, which their partners, with UK help, should ensure is done in as orderly a fashion as is practicable," he said,
He added that it would be in Europe's economic interest for "the misguided eurozone experiment to be dissolved altogether".
He said Grexit would "provide an important precedent for an agreement that 'ever closer' union cannot be absolute and that Mr Cameron's desire to see a number of key powers repatriated to the individual member states is both reasonable and thoroughly acceptable".
But the peer said: "My fear is that he will not seize this opportunity, but will join the chorus of support for maintaining the eurozone intact – for the time being, at any rate."
Bank closures in Greece have been extended until Monday and Greeks are limited to withdrawing just 60 euro (£43) per day after the imposition of capital controls.
British tourists have been warned to take sufficient cash to cover expected costs and emergencies and to ensure they have supplies of their usual prescription medicines in case of shortages.