Jones is "infatuated" with the 6-foot-5, 245-pound Pitts, according to ESPN's Chris Mortensen.
The 20-year-old is in contention to be the first non-quarterback offensive player selected in the draft, so the Cowboys would likely need to trade up from No. 10 overall to secure him.
Pitts caught 43 passes for 770 yards and 12 touchdowns in eight games during his final season with the Gators in 2020. He won the Mackey Award for the nation's top tight end and was named a unanimous All-American.
Schultz had a strong third season last year, catching 63 passes for 615 yards and four touchdowns despite Dak Prescott missing most of the season due to an ankle injury.
But Jones, who also acts as Dallas' general manager, has historically been unafraid to make blockbuster moves in the draft to land star players he covets.