Characterization of the speckle field structure is an actual task in non-destructive diagnostics of distant phase-inhomogeneous objects, like rough surfaces. In 2D, the speckle field singularities (optical vortices) are zero-intensity points, while in 3D space they can form complex structures, like closed links and knots. Traditionally, for visualization of such structures, interferometric techniques are used. In the case of diagnostics of speckle patterns on distant objects, the reference wave cannot be used, so non-interferometric methods become important. We propose the visualization of 3D speckle field zero lines using fluorescent nanoparticles, optically trapped at intensity minima regions. For such purposes, the refractive index of the particle should be less than that of the surrounding medium. The action of gradient optical force will move particles to the intensity minimum (or absolute zero in 3D), where the action of longitudinal scattering force is absent. The additional light source is used for particles' fluorescence excitation. The speckle field is formed due to the free space propagation at the Fresnel or Fraunhofer diffraction zone or in a focal region of the lens by focusing the object field. Visualization of 3D speckle field singularities can be produced in a high-volume region of nanoparticle solute, or reconstructed from the 2D planes, due to the axial scanning along the z-axis.