Following is a small derivation just so I can explain my question. The gravitational potential energy is:
$$(*)U_g = -\frac{GMm}{r}$$
And:
$$ \Delta U =-GMm(\frac{1}{r_{final}} - \frac{1}{r_{initial}}) $$
If some mass $m$ is taken a height $h$ above the ground, we get:
$$ \Delta U =-GMm(\frac{1}{R+h} - \frac{1}{R}) = \frac{GMmh}{R(R+h)} $$ approximating $h\ll R$ :
$$ \Delta U = \frac{GMmh}{R^2} $$ and if we denote $g=\frac{GM}{R^2}$ we get the familiar $$ \Delta U = mgh$$
That indeed goes hand-in-hand with (*), since the object went further from the center of the earth and therefore gained PE.
Now to the question: Does that mean we should always express the PE to be "more negative" the closer we are to Earth? I see some texts that present PE that gets bigger when you get closer to the Earth and that quite confuses me.