Intestinal villi (singular: villus) are small, finger-like projections that extend into the lumen of the small intestine. Each villus is approximately 0.5 -- 1.6 mm in length (in humans), and has many microvilli projecting from the enterocytes of its epithelium which collectively form the striated or brush border. Each of these microvilli are much smaller than a single villus. The intestinal villi are much smaller than any of the circular folds in the intestine.

Answer this question based on the passage: where are villi found in the small intestine? Let's have some stream of consciousness first.
This is the relevant information: Intestinal villi (singular: villus) are small, finger-like projections that extend into the lumen of the small intestine. So, the answer is the lumen.