USD rose slightly against most of its major rivals in the European session on Tuesday as investors awaited the U.S. inflation data for June (due at 12:30 GMT), hoping to get indications on the timing of the U.S. Federal Reserve's potential scale-back of bond buying. 

The U.S. Dollar Index (DXY), measuring the U.S. currency's value relative to a basket of foreign currencies, edged up 0.1% to 92.34.

Economists forecast consumer inflation to have increased 0.5% m/m last month, slightly decelerating from May's +0.6% m/m. On y/y basis, the CPI is expected to have advanced 4.9% after a 5% jump in the previous month. Excluding food and energy costs, inflation is seen to have gained 0.4% m/m and 4% y/y. 

There are worries that the hotter-than-expected inflation data could compel the Fed to begin tapering its asset purchases soon.

Market participants also digested the comments of the St. Louis Fed president James Bullard, who said in an interview with The Wall Street Journal (WSJ) that he thinks that “the time is right to pull back emergency measures”, given the facts “the economy growing at 7% and the pandemic coming under better and better control.” He also added that “we do want to do it gently and carefully, but I think we’re in a very good position to start a taper.”