The sentence is true, but not necessarily so.
It seems clear prima facie that a statement whose truth value you cannot really know might be something other than true. And that the mere possibility of it being something other than true does not imply that it is not actually true. Not everything that is possible, happens. (Note that you have chosen 'not true' and not 'false'. In the realm of modality, those are not necessarily equivalent. A proposition that depends on your moral stance might, when asked in general be neither true nor false.)
If you assume that you know it is false, you have a direct contradiction, because the impossible is not possible. So your option is that either you know it is true, or that you can't really know, so it might not be true, so it is still true.
So the statement is true, but that truth is not necessary -- it remains possible it could be otherwise, or it wouldn't be true in the first place.
What the question forces us to ask, I suppose, is whether what is actual is necessary. I am coming down on the side (opposite to
Aristotle) that necessity is a stronger requirement than actuality, so that even what is known to be true for some reason, could still be false in an alternative situation.
There could be a world where only what is necessary is true. In such a world, the modality of necessity and possibility vanishes, (at the expense of a lot of things being meaningless.) So it would devolve down to the original Liar's paradox, which has no truth value. So it could not be true. By at least one common definition of possibility, Kripke's, we do not live in that world, because we possess the ability to define coherent fictional worlds. It is only by this observed incident of our world, which is not necessary, that we can deduce the possibility of the statement's non-truth is not ruled out by the observation of its truth.
Unfortunately, that is hard to make clear. Formalizing it involves hokey nonsense. Here are a couple of approaches:
If we stick to the Kripke notion of 'possible', that something is possible if you can imagine a world where it is true. "It is possible that this sentence is not true." can be true.
Since the whole idea involves reference to text, it involves literal quoting. We can imagine the possible world where the literal text 'true' means 'interesting' instead of meaning true. We can then imagine that the sentence is uninteresting there, because it is here, at least to me. So we have found a world in which the sentence, as a piece of text, interpreted there would be true.
So the sentence "It is possible this sentence is not true." is true, if by 'this sentence' you mean the text of the sentence.
If you don't like the focus on the text, another way to look at it is that "It is possible this sentence is not true" means "It is not necessary that the sentence 'It is possible this sentence is not true.' is true." Well, in at least one logical world, the one where only what is necessary is true, it paradoxical, and therefore not necessarily true. So it is obviously not necessary for it to be true. That means this equivalent sentence is true and therefore the original sentence is true, just not out of necessity.
I will say again here, what I said at the top:
Note that none of this applies to "It is possible this statement is false." If you assume that is true, it is false. If you assume it is false, it is true, so it is false. If you assume it is neither true nor false, it cannot be false, so it cannot be true. In no case is it not in contradiction with itself.
Any argument that assumes these two statements are related, has not paid enough attention.