Athens and its creditors held tortuous talks over the weekend which failed to resolve the impasse over reforms, with European officials blaming Greece for failing to offer concessions in return for a final tranche of desperately-needed financial aid.
Greek banks sold off sharply, with most lenders in the country down over 10 percent on Monday, weighing on other European banking stocks.
Read MoreGreece on 'brink of disaster' as talks fail again
On the data front, all eyes this week will be on the conclusion of the Federal Reserve's latest Federal Open Market Committee's meeting on Wednesday.
While policy is expected to be left on hold, the Fed's updated economic forecasts will be watched for hints as to the likely timing of the first rate hike and the path for the pace of rate increases after that.
Empire manufacturing data showed the weakest level in more than two years as new orders fell, Reuters said. The New York Fed's Empire State general business conditions index fell from 3.09 in May to -1.98 in June, hitting its lowest level since January 2013.
May industrial production unexpectedly fell, dropping 0.2 percent in May.
Treasury yields fell, with the U.S. 10-year Treasury yield hitting a low of 2.31 percent and the 2-year yield holding below 0.70 percent. The German 10-year bund yield fell below 0.80 percent.
The National Association of Home Builders (NAHB) housing market index comes at 10:00 a.m.
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No major earnings reports are expected.