  We present preliminary results on the leading-twist
transverse-momentum-dependent (TMD) gluon linearity function, which is directly
connected to nucleon transverse-spin asymmetries originating from the density
of linearly-polarized gluons. The function is calculated in a spectator-model
framework for the parent proton and for the $f$-type gauge-link structure. Our
work represents a further step toward the definition of a complete set of gluon
TMD distributions at twist-2 that can be used to access the gluon dynamics
inside nucleons and nuclei at new-generation colliders.
