But at least for now, analysts seem more inclined to attribute the lack of a significant sell-off to confidence that ministers will find a way to satisfy the complicated political agendas on both sides.
"This can quickly turn sour for the euro if there is no deal today," said Susanne Galler, a strategist with Jefferies in London.
"The market consensus is for them to do a deal by the end of this week. But we think that if there's no deal today and the clock starts ticking then the euro will look increasingly vulnerable."
The euro gained a quarter of a percent against a broadly weaker dollar to trade at $1.1413. It was flat against the yen and 0.4 percent higher against Britain's pound.
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Analysts from one of the market's big four currency trading banks, Barclays, said there would be more volatility in store for the euro no matter the outcome. They said a Greek exit would be unambiguously negative for the euro zone.
"An agreement with significant concessions for Greece may raise the perception of risks in Spain, resulting in significantly greater downside risk for the euro," they said.
They also argue that a Greek deal with little relief for austerity or debt could potentially boost the euro in the near term and slow its descent in the coming months.
The dollar inched down 0.1 percent to 118.59 yen, from 118.70 at the end of last week and a one-month high of 120.48 set last Wednesday.
This week's Bank of Japan meeting is seen as unlikely to generate any new monetary easing, and positioning data showed speculators' net yen selling positions have shrunk to the lowest level since July.