The European Central Bank is likely to announce plans next month for phasing out the bond-buying program that has helped reinvigorate the eurozone economy, while the U.S. Federal Reserve is weighing how aggressively to retreat from its own easy money policies.

ECB President Margio Draghi signaled Thursday the bank could next month announce a plan to gradually end a program of asset purchases, known as quantitative easing or QE, in 2018. The Fed has already ended its bond purchases and is poised to announce plans in two weeks...