A drey — or dray — is a nest of a tree squirrel or a flying squirrel. Dreys are usually built of twigs, dry leaves, and grass, and typically assembled in the forks of a tall tree.They are sometimes referred to as “drey nests” to distinguish them from squirrel “cavity nests” (also termed “dens”).quirrels may also nest in attics or exterior walls of buildings, where a drey may be regarded as a fire hazard, as some squirrels have a habit of gnawing on electrical cables. At other times, squirrels may inhabit a permanent tree den in the hollow of a trunk or large branch.