Weatherspoon recently advanced to running after missing the entire 2014 season due to an Achilles tendon tear last June.
"He's a guy that's really, really focused on his rehab," Dimitroff added. "We need him back in this organization to help us go to another level. He's starting to move around."
Weatherspoon piled up 210 tackles, 7.0 sacks and 12 passes defensed from 2011-12. He was the Falcons' top defender before the Lisfranc, knee and Achilles injuries of the past three years.
With Dan Quinn bringing the 4-3 scheme back to Atlanta, Weatherspoon should be slated for a return to the weakside linebacker position in which he excelled.
Durability concerns would likely force Weatherspoon, 27, to settle for a "prove-it" deal on the open market. Perhaps the Falcons can coax him into a team-friendly deal by early next month.