A recently developed third order+second order perturbation density functional approximation (DFA) is briefly described. The applicability of this theory is demonstrated in the study of the density profiles of Lennard-Jones (LJ) fluid next to a large hard sphere (mimicking a colloidal particle) of various sizes. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. The chosen density and potential parameters for the equilibrium bulk LJ fluid correspond to the conditions situated at ‘dangerous’ regions of the phase diagram, i.e. near the critical temperature or close to the gas-liquid coexistence curve. It is found that the DFA theory performs successfully for both supercritical and subcritical temperatures. It is also shown that the ‘universality’ of the adjustable parameter associated with this theory holds also in the present case of a large spherical particle as a source of external potential. Here the term universality means independence of this parameter on the particular external field responsible for the generation of a non-uniform density profile of the fluid. This DFA results can be used as a useful starting point for further investigation of solvent-induced excess potential of mean force in the similar systems.