My reasoning is that all matter is made of quarks + the space in between them. So therefore, among matter, a single quark should be the densest object. I'm not sure for non-matter though; I'm also not sure about singularities.
This is the table of elementary particles of the Standard Model of particle physics.
All these particles are point particles, and in a mathematical sense, the fact that many of them are assigned a mass would be considered as a singularity in density, but that is not the way it happens in the microcosm of quantum mechanics. The concept of mass density has no meaning for single particles ,in a framework where everything is described by a probability and in addition is ruled by quantum mechanics laws.