In general, yes. But it has been done only for static friction coefficients.
The manner of which two surfaces in contact interact is highly investigated by the Tribology community.In particular, the field exploring the mechanics of the interaction is called contact mechanics.
Tackling problems of contact mechanics analytically/numerically is often done by solving the elasticity equations. By predicting quantitatively the forces and deformation of the bodies in contact, the coefficient of friction can be calculated. Much research has been carried on the subject: starting from Hertz's groundbreaking work, to more contemporary papers such as A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces, and Static Friction Coefficient Model for Metallic Rough Surfaces.