Walters, 19, promoted to the senior squad this summer and looking to make his first-team breakthrough, is waiting to learn if he needs an operation to resolve cartilage damage. He signed his first professional contract - a two-year deal - in March.
Former Reading forward Hunt, a free signing in the summer of 2013, was hindered by hamstring trouble last season when he was restricted to 20 appearances. Both players were withdrawn during the recent friendly defeat at Mansfield.
Leeds will continue their pre-season preparations at Chesterfield on Saturday, with boss Dave Hockaday promising to field his strongest line-up against Paul Cook's newly-promoted League One side.