But Mr Dijsselbloem struck a cautious note, saying that, while it may be possible to begin the technical work of determining which parts of the current bailout the Tsipras government would agree to continue and which reforms it seeks to scrap, reaching a political agreement on Monday would be more difficult.
"I am very cautious on the political side," Mr Dijsselbloem said. "It is going to be very difficult. It is going to take time. Don't get your hopes up yet."
Mr Tsipras, who has repeatedly insisted he would not allow the current bailout to continue, called efforts to pressure Athens into accepting the commitments of the current bailout a "scare campaign". He noted that none of the dire predictions of his critics have come true.
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"In the last days, we listened about scenarios about a Greece bankruptcy if Greece wouldn't accept an extension of the bailout program," Mr Tsipras said. "But no devastation, no catastrophe occurred, as you can see."
Although the Greek bailout runs through to the end of the month, Mr Tsipras must request an extension by Monday or else there will not be enough time for eurozone parliaments to approve the deal.
"There's not much time because there are rules in certain countries whereby if the programme is changed or extended whatever the words, parliament needs to vote on it," said François Hollande, French president. "The Greek government is conscious of that."