Could there ever be an end to knowledge? Not an end to our ability to reason, or to have opinions, or to use logic to figure things out on a daily basis. But knowledge itself, can there be an end to it?
I'm going to say 'no'. While omniscience might be hypothetically possible in principle (assuming that the universe cooperates), it would seem to be impossible for beings like ourselves.
To possess all possible knowledge, the universe would have to be finite, not only in its spatial temporal cosmological extent, but also in the amount of detail discoverable on the microscale, by looking closer and closer at things. If that wasn't the case, we could just keep discovering new facts indefinitely by looking further out or by using stronger microscopes. More radically, we would have to have similar information about any other universes or modes of being that might exist, separate and disjoint from our own universe. (Our space-time continuum might not contain all of reality.)
And the universe would also have to be finite in a more conceptual sense, in terms of the principles such as mathematical principles, logical principles and so-called "laws of physics" applicable within it. We would need to have some way of accounting for the existence of logic and the 'laws of physics' and for explaining why the the universe conforms to them and why they are what we observe them to be. We would also also have to have some reason to reject emergence, the appearance of genuinely new and unpredictable phenomena (arguably including biological life or minds) within a universe. (If unforseen possibilities are being realized unpredictably, knowing how things will unfold in the future becomes problematic.) And finally, we would have to have an answer to the ultimate question: Why does existence exist at all? (My own feeling is that last one is unanswerable in principle, since all attempts to do so would be circular.)
Those are metaphysical considerations. There are also practical considerations.
A hypothetical omniscient knower would have to have some way of learning every possible detail about every hidden corner of the universe. It would have to know as much about every exoplanet and every barren asteroid in the billions of galaxies as we can hypothetically discover about Earth. It would have to have some way of learning all the applicable principles everywhere. Time, space and things like black-hole event horizons create difficulties for that. The possibility that something might exist outside our space-time continuum that we would need to know about creates even bigger problems. So access to information creates huge constraints.
That hypothetical omniscient knower would have to have the raw memory and processing power to process that incredible amount of information and would have to have the cognitive powers necessary to conceive of all the abstract relationships in all of it. (Mathematical, logical...) Here on Earth, cockroaches don't have the cognitive firepower to even conceive of Schroedinger's equation. So it might be most realistic to expect that there might be aspects of the universe, necessary to achieving a full understanding of it, that will always be beyond us, that human beings can never even suspect, let alone know.