Of course, this great novel is already well and truly part of the Western Canon, and rightfully so, from my perspective. As #2 identifies, it captures a particular period of history, The Jazz Age, and embodies it in literary form, making a number of very profound comments about wealth, social standing and decadence. The feeling of sadness and palpable loss that comes through from the text makes this novel a lament for what could have been.
To me, the value of The Great Gasby to the literary canon (for it is part of the Western literary cannon, whether one thinks it should or not, as has been pointed out) is that it captures perfectly the post-World War I era known as the "roaring twenties." It depicts the excessive wealth of both the newly rich and the inherited rich (new money and old money). In contrast, we see the ashen existence of those without money. We see the extravagances of living in a post-war world, and we see the careless behaviors and corruptions of those who have nothing in particular for which to live. Fitzgerald was part of a disillusioned group of writers who reflected the Lost Generation and who exiled themselves from their country (most went to Paris) because they didn't like what they saw. This sense of dreams both realized and unfulfilled make this novel an iconic reflection of the era.
I would say that Fitzgerald's work is already accepted into the American canon of literature. If we examine it as whether or not it should be worthy of being included in the canon of Western Literature, we can use the same analysis as to why it is included in the American echelon of great works. The book does an excellent job of articulating what life is like with wealth and without it, identifying specific challenges in both realms. Individuals can relate to it because of its quality of discussing what wealth resembles and how life is established with and without its presence. I think that one reason why there might be reticence to including it in the Western canon is because it speaks to the condition of being "American," while other works in the Western canon seek to broaden its appeal in being more universal. However, I do believe that the same ideas of being able to articulate a condition where people address consciousness in terms of possessing wealth and coveting it could help to make the work more universal in reach and appeal.