Clowney first visited the team on Wednesday and is now expected to return again today as the two parties size each other up before next month's Draft.
The defensive end has been widely tipped to be one of the top picks in this year's Draft and has already expressed his desire to be chosen first overall.
The Houston Texans currently have the number one pick, although Falcons general manager Thomas Dimitroff has hinted that the team could trade up from their sixth overall pick.
Clowney has also stated that the Falcons would be his preferred destination, urging them to trade up to select him first.
It is understood that Clowney will not be working out on his visit to the team having decided against doing any more private workouts after fellow Draft prospect Brandon Thomas tore his ACL during a visit with the New Orleans Saints.