Greek and broader European stocks turned higher on reports that Greece was being "more constructive" in talks, according to Reuters.
This came after a spokesman for the Greek government said the country needed a deal agreement with creditors by the end of the month, as fears grow that the country is on the verge of bankruptcy.
Meanwhile a letter from the country's officials to the International Monetary Fund revealed that Greece came close to defaulting on a 750 million euro ($860 million) repayment last week, according to a report by Greek daily newspaper Kathimerini that was confirmed by the Financial Times.
"The day of reckoning is coming for Greece," Michael Hewson, chief market analyst at CMC Markets UK, told CNBC.
"We've been worried about an end-game for some time and the letter to the IMF shows just how serious the position in Greece is."
Read MoreGreece's 'endgame' in sight; bond yields soar
The euro declined to around $1.135 on Monday.
Fears about Greece also weighed on U.S. stocks on Monday, which traded in a narrow range. However, both the Dow Jones Industrial Average and the benchmark S&P 500 indexes high record highs during the session.
In Asia, a new trading week ushered in another mixed trading session, as investors' confidence wavered following data that showed further declines in China's house prices.