Public remarks by Draghi and other ECB officials since the May meeting have reinforced expectations that action will be forthcoming.
The euro has fallen 2% against the dollar as a result, bringing some relief to exporters and easing the pressure on prices by making imports more expensive.
So what will Draghi do?
Cutting the main interest rate to 0.15% or even 0.10% looks like a done deal. Many economists also expect the central bank to take a step into the unknown by cutting its deposit rate from zero into negative territory.
That would have the effect of charging banks for parking spare cash with the ECB, in theory providing an incentive to lend that money to firms and consumers instead. But there is a risk that the experimental move could backfire.
There's also a good chance the ECB will offer cheap, long term loans to banks, possibly with the explicit aim of boosting lending to the thousands of small businesses that form the backbone of the European economy and lack access to other sources of finance.
Draghi is likely to stop short of launching a full-blown quantitative easing progam, but will keep the option firmly on the table.