George and Lennie are bonded by a dream of owning a piece of land. This dream, though not the sole bond connecting the two men, allows both George and Lennie to believe that their current state as itinerant farm laborers will not last forever.
In regards to the American Dream, the vision of land ownership and self-determination shared by George and Lennie is direclty in line with the ideals of self-improvement and personal franchise implicit in the American Dream.
If we define the American Dream as an aspiration for improved financial and social status, we can read the vision of George and Lennie as just this - an aspiration to rise up the social-commerical ladder to a position where they can make their own decisions (how much to work everyday, when to take a break, etc.).
One of the themes of Of Mice and Men concerns the barriers between the workers and this dream of self-determination.
Although George and Lennie have their dream, they are not in a position to attain it. In addition to their own personal limitations, they are also limited by their position in society. Their idealistic dream is eventually destroyed by an unfeeling, materialistic, modern society.
George and Lennie want to own their own land (farm), without having to work for other people. Lennie wants to tend the rabbits.