Wilkins, a redshirt sophomore who was the backup to Mike Bercovici last year, emerged from a three-way competition with redshirt freshmen Brady White and Bryce Perkins, though Perkins was eliminated early in fall camp due to injury.
Graham, appearing on Doug & Wolf on 98.7 FM, also said it's possible White will see action against NAU.
None of the three quarterbacks has thrown a pass in college.
"We have great confidence in Brady as well, but Manny's our guy," Graham said. "He'll run out with the first group and we'll go from there."
The Sun Devils play host to Texas Tech on Sept. 10.