Greece, which last week defaulted on a major loan to the International Monetary Fund and has imposed capital controls to limit an exit of cash, is in uncharted territory following Sunday's referendum.
The country's outspoken Finance Minister Yanis Varoufakis resigned on Monday, removing an obstacle to talks with Greece's creditors.
Read More 'Toxic' Varoufakis is out: Time for a deal?
The European Central Bank meanwhile holds a conference call later in the day to decide how long to keep Greek banks afloat, while euro zone leaders are to hold an emergency summit on Greece on Tuesday.
"The key is not so much when talks resume (but) if the ECB increases loans," said Peter Cardillo, chief market economist at Rockwell Global Capital.
The Institute for Supply Management's June service sector survey is due out at 10:00 a.m. ET and may take investors' focus briefly away from Greece to the U.S. economic outlook.
After last Thursday's softer-than-expected U.S. non-farm payrolls report, expectations for a September interest rate rise from the Federal Reserve have been scaled back.
Read MoreWhen markets get past Greece, they'll watch Yellen
Elsewhere, U.S. Treasury yields were broadly lower as jitters over Greece sent investors fleeing into safe-haven bonds. The yield on the benchmark 10-year note was down 8.6 basis points at 2.30 percent.
The dollar edged higher against the euro at 1.1013 and down 0.1 percent at 122.74 yen.
Ahead of the unofficial start of earnings season this Wednesday, A Schulman posts results after the close.
In other corporate news, Humana agreed to be bought by rival Aetna for $37 billion in cash and stock. Humana shareholders will receive $125 in cash and 0.8375 Aetna shares for each share they now hold.
Seritage Growth Properties, the real estate investment trust created by retailer Sears Holdings, will begin trading Monday on the New York Stock Exchange. Sears said the rights offering of Seritage shares expired last Thursday and that it was oversubscribed.
Read More Early movers: HUM, SRG, AAPL, POT, BABA, MCD, YUM & more
Dollar Tree has received U.S. Federal Trade Commission approval to acquire rival Family Dollar Stores after a nearly year-long review. The combined company will need to divest more than 300 stores. Dollar Tree expects the deal to be completed today.
—CNBC's Peter Schacknow contributed to this report
Correction: This story has been updated to reflect that only A. Schulman reports earnings on Monday.