The decision to base the agency in Amsterdam after Brexit was decided by drawing lots last November. It is currently based in London.
However, there are concerns about the planned move.
Officials say that, in light of concerns raised by Executive Director Guido Rasi on Monday about the temporary space available in Amsterdam, Milan will try again for a chance to host the agency.
The European Commission has adopted a proposal urging member states to make drinking water fully accessible to all citizens.
Figures suggest 20 million Europeans have no access to healthy drinking water.
This is said to be a particular problem in countries with vulnerable and marginalised communities.