Brainard, a member of the policy-setting Federal Open Market Committee (FOMC), will speak in Washington D.C. at 10 a.m. ET on the U.S. economic outlook and monetary policy. Markets remain focused on the Fed for hints as to when the long-awaited hike in interest rates could occur.
Tuesday will be a quiet day for U.S. data, with factory orders for April at 10 a.m. EDT and auto and truck sales for May at 5 p.m.
The nation's automakers release May sales figures today, and while analysts at Edmunds.com expect the annual sales rate to come in at a relatively strong 17.4 million units, overall sales are expecting to be down 0.9 percent compared to May of 2014.
Consensus forecasts for April factory orders are calling for a 0.1 percent decline. Factory orders had risen 2.1 percent in March.
Of greater interest may be inflation data from the euro zone, which came in at 0.3 percent in May. This was higher than the 0.2 percent forecast and will help waylay fears of a deflationary spiral in the region.
The U.S. dollar hit a 13-year high against the Japanese yen on Tuesday, piercing a key psychological level to trade at 124.91 yen.
Fears about Greece remained in the backdrop, with no reforms-for-aid deal in the offing and a 300 million euro ($327.9 million) repayment to the International Monetary Fund due on Friday.
—CNBC's Peter Schacknow contributed to this report.