The story is rather short - one or two A4 pages, and I read it in a weekly (not in English) some 30-33 years ago.
The setting is a room, with a man and a pet (either a cat or a dog). The pet starts speaking and the man is taken aback, because the pet explains that humanity has run its course, and will degrade mentally to the point of not being able to take care of itself. The story concludes with the pet saying that the man shouldn't be afraid or worried, because the pet will take good care of him.
As far as I can tell, there was no uplifting, telepathy or magic involved.