Of Mice and Men is a novel full of dreamers. Fundamentally, everyone in it is ultimately dreaming of a better life—from Curley's wife, who dreamed of being "put . . . in the movies," to George and Lennie, who dream of living on a farm somewhere they own, with several acres of land and animals of their own, including Lennie's beloved rabbits. George and Lennie are big dreamers, with a defined and oft-repeated dream, but others are sucked into this dream, too—even old Candy suggests he could "hoe the garden" on the farm one day. Everybody in the book wants to believe that something like a dream might one day be possible.
So, who is the "biggest" dreamer? And how do we define "biggest"? I might argue that the "biggest" dreamer is not just the person with the biggest dreams—after all, George and Lennie share the same big dream, which others also find appealing—but the person who is least disillusioned about these dreams over the course of the novel.
That being the case, I would assert that Lennie is the biggest dreamer. A developmentally delayed idealist, Lennie doesn't ever realize, as George does, that their dream is only a dream and unlikely ever to become reality.
Context and citation for this can be found early in the novel. Lennie tells George that he "remember[s] about the rabbits," an element of the dream he fixates upon. Lennie wants to lose himself in the dream even when it is frustrating to George (when George tells him the dream and the rabbits are all he ever thinks about). Lennie's capacity to want what doesn't exist extends far beyond George's, because George is really a rationalist—as he says, "whatever we ain't got, that's what you want."
In the explication and interpretation section, we explain what we've pointed out and show how it supports the assertion. The dream of the farm is one shared by George and Lennie and a story which George has often repeated. George really wants to believe that he and Lennie could one day move to a farm together, and own it, and be their own masters, but it's not so clear that he really believes it. Lennie, on the other hand, believes wholeheartedly. His childish nature means that he is able to commit himself to these dreams, without ever recognizing their limitations.
In the conclusion, we summarize what we've stated above and drive the point home. George and Lennie share a pipe dream of owning a farm together, but the difference in their natures means that this represents different things to each man. George wishes this future could come to pass; Lennie really believes that it might. And, therefore, while George ultimately recognizes that this is not something he will ever achieve, Lennie goes to his death believing that dreams are possible.