The 22-year-old Saddlers academy product agreed a two-year contract in May, and his existing deal has now been extended by a year.
"This club is amazing for bringing youngsters through," Morris is quoted by BBC Sport as saying.
"You only have to look at some of the names who have passed through the door in the last five, 10, 15 years. It's a place where you will get your chance and it's up to you then to take it."
Morris has found the net four times for Walsall this season.