The closest I've seen in the Pali canon to what you're describing is in the Mulapariyaya sutta. I am not sure if it constitutes the idea of "cannot be attained," but the Buddha here describes Unbinding as this:
A monk who is a Worthy One, devoid of mental fermentations... directly knows earth as earth. Directly knowing earth as earth, he does not conceive things about earth, does not conceive things in earth, does not conceive things coming out of earth, does not conceive earth as 'mine,' does not delight in earth. Why is that? Because, with the ending of delusion, he is devoid of delusion, I tell you.
He directly knows water as water... the All as the All...
He directly knows Unbinding as Unbinding. Directly knowing Unbinding as Unbinding, he does not conceive things about Unbinding, does not conceive things in Unbinding, does not conceive things coming out of Unbinding, does not conceive Unbinding as 'mine,' does not delight in Unbinding. Why is that? Because, with the ending of delusion, he is devoid of delusion, I tell you.
My limited understanding of this is that an Arahant may be aware that they have come to an end of suffering, but nevertheless they do not have a positive (or any) feeling towards being an Arahant, and they also do not feel ownership over this quality. It might depend on what "supramundane" refers to, but these seem to at least be unconventional aspects of an attainment listed in the sutta above.