Futures for the 30-stock index inched up 27 points, or 0.1%, to 39,024.
Futures for the S&P 500 were unchanged at 5,206.50.
Futures for the NASDAQ Composite lost 32.5 points, or 0.2%, to 18,162.
Disney shares were flat after the media and entertainment giant posted better-than-expected quarterly figures. Its streaming business nearly broke even for the quarter.
Investors on Monday carried over the bullish market sentiment from Friday, when the latest nonfarm payrolls data showed that job growth came in below expectations in April and unemployment ticked higher. The results alleviated concerns that the economy was too hot and raised optimism around rate cuts from the Federal Reserve.
In Japan, the Nikkei 225 returned to trading with a gain of 1.6%, while in Hong Kong, the Hang Seng Index backed off 0.5%.
Oil prices gave up 0.31 cents to $78.17 U.S. a barrel.
Gold prices sank seven dollars to $2,324.20 U.S. an ounce.