No that is not currently possible. The Scandinavian countries could do it, but most of the rest of EU cannot, because they don’t have a solid enough infrastructure to not have old fashioned cash.

When we talk cash here, we mean physical cash as in non digital payments.
But even though EU as a whole isn’t ready to go cashless yet, they can still make limitations on cash payments like the ones we have here in Denmark.
And that can be used to increase national oversight of how money is being used.