We briefly overview several operator definitions of gauge-invariant unintegrated (transverse momentum dependent) gluon density function available in the literature, with emphasis on the structure of the Wilson lines or loops. We propose a gauge-invariant formulation of a generating function with maximal path-dependence, which, as distinct from the other approaches, includes an arbitrary Wilson loop, not necessary containing light-like segments, and with no reference to any factorization scheme. After suitable area differentiation, this object can be associated with fully unintegrated gluon distribution function, which allows to apply this approach in lattice simulations.