Spreading of a tiny macroscopic droplet of a nonvolatile, completely wetting liquid over a hat solid is considered. A liquid in creeping is subjected to capillary forces and long-range molecular forces. The droplet may be surrounded with a precursor wetting film. This paper deals with the problem of determining of the microscopic parameter that influences the interface shape near the apparent line of wetting; this is regarded as the inverse problem in the hydrodynamics of wetting. If the system includes a precursor film, the microscopic parameter coincides with the maximum thickness of the film. A series of inverse equations for the microparameter is obtained, which relate it to, first, the current geometric parameters of the macroscopic drop part and, second, the spreading time. A method for determining how the microparameter depends on the wetting line speed is proposed. The theory expands the opportunity to perform macroscopic measurements and reveals additional parameters. The inverse relations may be used to experimentally study the growth of the maximum thickness of a precursor film during drop spreading,