Some people went looking for it in Iceland a few years ago. The theory states that it isn't actually a grail, but scrolls with the wisdom for eternal life. There was an Irish Monk settlement briefly in Iceland prior to the Vikings arriving there. The Monks may have taken some Christian treasures and hid them in Iceland, since it was uninhabited at the time and the Vikings kept raiding England, Scotland, Ireland and whatever other nations were on these islands at the time.
That's what I heard.
The first mention of the holy grail appears in the 12th century writings of Chrétien de Troyes. Chrétien however, describes a large wide dish that provides food and sustenance. Curiously he associates it with salmon which I'll discuss below. None of this appears in Biblical texts.
Compare this with the grail as a depicted in modern pop culture and you'll see they are not the same thing. Early Christianity often merged pagan beliefs with Christianity and many believe this is a Celtic symbol surviving into the christian era. Not everything tied to Christianity is actually Christian - see Christianity.com for their debunking of the grail.
To add to the confusion, Chrétien died before completing his work - leaving other scholars to decipher what he was talking about. A symbol, the elixir of life or an actual grail? The suggestion that the grail was the same cup used by Christ was an interpretation of another writer, Robert De Baron after Chréttien's death. But that was a drinking vessel. Other writers claim the grail is a stone with a serpent inside of it.
Celtic Myths of cauldrons that provided infinite sustenance are worth noting since France has a Gaulish heritage - and the in the mythology of the Gaels, a salmon was said to swim in the 'well of knowledge', that same salmon was associated with the tree of life - the mythical 'salmon of knowledge' who ate acorns which fell from the tree of life and being 'all knowing' and wise. If you ate the salmon you would gain the salmons all knowing wisdom, ie a Christianised Celt might interpret that as answers to the meaning of life itself.
Now consider that 200 supposed grails existed - as well as Crétien's description of the grail being large enough to serve a whole salmon. Is it possible these grails are merely pagan sacred relics saved from destruction from Christians by being adopted into Chistrian lore? Perhaps even melted down and reshaped using Christian iconography? Or instead are entirely made in the Christian era to symbolise the cup of Christ?
Irish monks may very well have hid one such object in Iceland but it's safe to say it is not the cup used during the last supper. Other Christian grails might be derived from Roman myth or Mesopotamian myth - but anything possessed by Irish monks was likely local.
TL;DR the grail is a metaphor - any vessel held by any Religious Order was a symbol of that metaphor, not the grail itself.