My first approach was to try with Menu Items Extra and Simple menu icons but the images are not rendered. So I thought that this could be related to the menu module I've been working with so I tried with Superfish and Megamenu. But again it didn't work. I must say that Megamenu was the closest one but since it requires Font Awesome Icons I cannot use my designer's icons with this module.
My last try was to add a class to each parent menu link with Menu Link Attributes so I could add the images via CSS. The huge problem with this approach is that if I replace the parent menu item name with an image it will also appear on mobile making the menu to look massive.
Any ideas on how to add the images?