According to the source, Clowney's session with the Falcons, set to take place at South Carolina, is "not really a workout."
Although it was earlier reported by ESPN that Clowney would be running through some drills, he will be not be working out, according to ProFootballTalk.
Word surfaced of Clowney being done with private workouts after another draft prospect, Clemson offensive lineman Brandon Thomas, tore an ACL during such a workout with the New Orleans Saints. However, agent Bus Cook told USA Today that Clowney could go through one more abbreviated session prior to the NFL Draft. Cook's words likely were an indication of the Falcons' intentions to meet with Clowney while also reportedly conducting a workout with another South Carolina prospect, wide receiver Bruce Ellington.
Clowney has already expressed a desire to be the first player selected by the Houston Texans. The Falcons currently hold the sixth overall pick, and general manager Thomas Dimitroff said he is always open to trading up. Dimitroff traded five draft picks in 2011 to move up for top receiver Julio Jones, the sixth-overall pick that year.
Dimitroff spoke highly of Clowney back in February.
"Obviously, he is an incredible talent with wild upside," Dimitroff said. "He's going to be a very big contributor on a football team from day one. We all know that. The league knows that. He has the potential to be one of the marquee-type pass-rushers."
During this year's NFL combine, the possibility of playing for the Falcons was posed to Clowney.
"I wish they could trade up for me," Clowney told ESPN.com. "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, a native of Rock Hill, S.C., is considered the most athletically gifted player in the draft at 6-foot-5 and 266 pounds.
The Falcons sorely need help at pass-rusher after finishing tied for 29th in the league last season with just 32 sacks, and had the league's worst third-down defense. Although the Falcons are preparing for more of a 3-4-base defensive scheme, the multiplicity they seek on defense would make Clowney a fit regardless.
If the Falcons stand pat at No. 6, they seem likely to target one of top three offensive tackles: Auburn's Greg Robinson, Texas A&M's Jake Matthews, or Michigan's Taylor Lewan. Buffalo pass rusher Khalil Mack and Clowney appear the be the other players on their first-round wish list. All five players visited the Falcons in the past two weeks.
CBS Sports earlier reported Clowney's scheduled session with the Falcons on Friday.