The 21-year-old, who is considered one of the best prospects in the Draft after an outstanding college career with the Gamecocks, believes that the Falcons would be a good fit for him.
"I wish [the Falcons] could trade up for me," Clowney told ESPN.
"I hope I don't fall to No. 6. I like Atlanta — a lot. They're pretty good, they've got some guys from South Carolina on the team, also. And it's close to home."
Clowney notched 24 sacks during his three years with South Carolina.