The short answer is it's not present in the painting.
Why? Best guess: mention of the Holy Grail is not found in the canonized Gospels. There would not have been a practical reason to represent it in the composition. Leonardo's commission was to paint a wall in a Church community. On the surface, at least, he stuck to accounts of The Last Supper as found in the Gospels. This would be entirely within keeping of the extremely detailed artistic contracts that were standard procedure during what is now known as "the Renaissance".
The Holy Grail is a literary invention. There are dozens of hypotheses as to (1) where the story originated, (2) whether or not it even has Christian meaning, and (3) what sort of item this particular grail is supposed to be. Is it a chalice? A cup? Platter? Stone? Reliquary? (In the interest of fairness, I suppose we must now add "uterus" to this already long list.) Arguments for/against the validity of any of these (singular or combined) hypotheses can be constructed. However, the only certainty that can be stated about the Holy Grail is that it is a fictitious device, employed by writers.
Now, whether or not Leonardo believed that the Holy Grail existed is another matter entirely. The first written accounts of it only preceded his lifetime by 300 years, and Malory's Le Morte D'arthur was contemporary to Leonardo. Maybe he read Malory or an earlier version. For what it's worth, Leonardo tended to lend more credence to that which he'd observed firsthand, than to that which he'd read or heard. In my opinion, it's hard to imagine he'd have been so enamored with what amounted to an urban myth, that he'd take the time and trouble to hide reference to it in the Last Supper. That's just my opinion, though.
So, yes, perhaps he'd read the stories, perhaps he believed they had merit, and perhaps he painted some form of hidden Holy Grail in the Last Supper, somewhere. Three instances of "perhaps" in one sentence would seem to send logic out on a rather shaky limb. But it's hard to know, lacking official word from Leonardo on the topic, isn't it?
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