[8] Gresham was also an outstanding basketball player before giving it up after the ACL knee injury, and to pursue his career in football as an Oklahoma Sooner.

[11] The Ardmore Tigers returned to the Class 5A boys basketball final game for 2004, but lost to the Oklahoma City Southeast Spartans, 60–55, and finished with a 25–3 record.

In the game Gresham stole the ball and dunked it making the score Tulsa Washington–37 Ardmore–34 with 5:25 left in the third quarter, but he was penalized with a technical foul for hanging on the rim.

[18] He averaged 26.5 points-per-game (PPG) in the state tournament his junior season and was named to the Class 5A Boys All-Tournament First-team, including a career-high 39-points in a quarterfinal 78–74 win over Oklahoma City John Marshall.

[24] National analyst Jeremy Crabtree of Rivals.com called Gresham a "slam-dunk" prospect along with Oklahoma City Southeast defensive lineman Gerald McCoy.

His 52 receptions set a franchise record for catches by a rookie tight end, and ranked him third on the team (tied with Jordan Shipley).

Gresham missed two games of his second season with injuries, but still made an improvement in every statistical category, catching 56 passes for 596 yards and six touchdowns.

The season resulted in Gresham being named to his first Pro Bowl, replacing the Super Bowl-bound Rob Gronkowski and first alternate Aaron Hernandez.

Gresham was named to his second consecutive Pro Bowl and joins Mike Ditka and fellow Sooner Keith Jackson as the only tight ends in NFL history to have over 50 receptions in the first three years of their career.

Gresham's production was reduced in 2013 as he found himself sharing the starting spot with rookie tight end Tyler Eifert, but he still had a solid year, catching 46 passes for 461 yards and 4 touchdowns in 15 games.

[36] On March 13, 2016, Gresham turned down four-year offers from both the New York Jets and Chicago Bears to stay with the Cardinals on a one-year deal.