I don't think you'll find any simple correlation or relationship, because there's too many variables in both terms.
Firstly, there are various ways of measuring the friction; one example is the
Canadian Runway Friction Index. Different methods use different measurement techniques and will return different values for similar surfaces.
Secondly, aircraft friction coefficients are usually calculated at the "aircraft level", which is to say that factors such as the weight distribution between braked and unbraked wheels and the effectiveness of any anti-skid system are encompassed by the aircraft mu. Different aircraft will brake more or less effectively on the same surface, and would have different aircraft mu as a result.
Even if you tried to narrow the comparison by specifying both the measurement technique and the aircraft, I suspect it still would be at best a rough-and-ready comparison; it's not an exact science.