There is no such thing as "absolute" potential energy. Potential energy is always "relative" to some zero-point. Any mass has potential energy 0 relative to its own position. But being "on the surface of the earth" could mean at the top of a mountain! An object, of mass m, on the surface of the earth, will have potential energy 10mg relative to the bottom of a hole 10 meters deep. It will, in general, have potential energy mgx relative to a position x below it or -mgx relative to a position x above it- as long as x is small enough that we can treat g as a constant.